id
int64
1
14M
domain
stringclasses
6 values
topic
stringclasses
23 values
subtopic
stringclasses
37 values
difficulty
int64
1
8
unit_type
stringclasses
3 values
title
stringlengths
14
86
content
stringlengths
203
553
key_equations
stringclasses
23 values
prerequisites
stringclasses
29 values
learning_objective
stringclasses
37 values
3,201
mathematics
algebra
linear_relation
2
worked_example
Evaluate linear function y = 4.611 x + 4.829 at x = 3.061
The linear relation y = m x + b with slope m = 4.611 and intercept b = 4.829 evaluated at x = 3.061 yields y = 18.94. Linear models appear throughout science whenever a rate of change is approximately constant.
y = m x + b
basic arithmetic
Evaluate and interpret a linear function in a scientific context.
3,202
mathematics
algebra
linear_relation
2
worked_example
Evaluate linear function y = -3.326 x + -17.59 at x = 8.436
The linear relation y = m x + b with slope m = -3.326 and intercept b = -17.59 evaluated at x = 8.436 yields y = -45.65. Linear models appear throughout science whenever a rate of change is approximately constant.
y = m x + b
basic arithmetic
Evaluate and interpret a linear function in a scientific context.
3,203
mathematics
algebra
linear_relation
2
worked_example
Evaluate linear function y = -2.267 x + -9.964 at x = 3.6
The linear relation y = m x + b with slope m = -2.267 and intercept b = -9.964 evaluated at x = 3.6 yields y = -18.13. Linear models appear throughout science whenever a rate of change is approximately constant.
y = m x + b
basic arithmetic
Evaluate and interpret a linear function in a scientific context.
3,204
mathematics
algebra
linear_relation
2
worked_example
Evaluate linear function y = 4.992 x + 13.7 at x = -5.745
The linear relation y = m x + b with slope m = 4.992 and intercept b = 13.7 evaluated at x = -5.745 yields y = -14.98. Linear models appear throughout science whenever a rate of change is approximately constant.
y = m x + b
basic arithmetic
Evaluate and interpret a linear function in a scientific context.
3,205
mathematics
algebra
linear_relation
2
worked_example
Evaluate linear function y = 3.407 x + -8.748 at x = -6.772
The linear relation y = m x + b with slope m = 3.407 and intercept b = -8.748 evaluated at x = -6.772 yields y = -31.82. Linear models appear throughout science whenever a rate of change is approximately constant.
y = m x + b
basic arithmetic
Evaluate and interpret a linear function in a scientific context.
3,206
mathematics
algebra
linear_relation
2
worked_example
Evaluate linear function y = 0.3409 x + -17.2 at x = -8.206
The linear relation y = m x + b with slope m = 0.3409 and intercept b = -17.2 evaluated at x = -8.206 yields y = -20. Linear models appear throughout science whenever a rate of change is approximately constant.
y = m x + b
basic arithmetic
Evaluate and interpret a linear function in a scientific context.
3,207
mathematics
algebra
linear_relation
2
worked_example
Evaluate linear function y = 1.984 x + 13.22 at x = 4.501
The linear relation y = m x + b with slope m = 1.984 and intercept b = 13.22 evaluated at x = 4.501 yields y = 22.15. Linear models appear throughout science whenever a rate of change is approximately constant.
y = m x + b
basic arithmetic
Evaluate and interpret a linear function in a scientific context.
3,208
mathematics
algebra
linear_relation
2
worked_example
Evaluate linear function y = 4.988 x + 15.13 at x = -5.783
The linear relation y = m x + b with slope m = 4.988 and intercept b = 15.13 evaluated at x = -5.783 yields y = -13.72. Linear models appear throughout science whenever a rate of change is approximately constant.
y = m x + b
basic arithmetic
Evaluate and interpret a linear function in a scientific context.
3,209
mathematics
algebra
linear_relation
2
worked_example
Evaluate linear function y = 0.0482 x + 12.08 at x = 7.679
The linear relation y = m x + b with slope m = 0.0482 and intercept b = 12.08 evaluated at x = 7.679 yields y = 12.45. Linear models appear throughout science whenever a rate of change is approximately constant.
y = m x + b
basic arithmetic
Evaluate and interpret a linear function in a scientific context.
3,210
mathematics
algebra
linear_relation
2
worked_example
Evaluate linear function y = 4.454 x + 5.407 at x = 9.593
The linear relation y = m x + b with slope m = 4.454 and intercept b = 5.407 evaluated at x = 9.593 yields y = 48.13. Linear models appear throughout science whenever a rate of change is approximately constant.
y = m x + b
basic arithmetic
Evaluate and interpret a linear function in a scientific context.
3,211
mathematics
algebra
linear_relation
2
worked_example
Evaluate linear function y = 2.078 x + -9.079 at x = 3.246
The linear relation y = m x + b with slope m = 2.078 and intercept b = -9.079 evaluated at x = 3.246 yields y = -2.337. Linear models appear throughout science whenever a rate of change is approximately constant.
y = m x + b
basic arithmetic
Evaluate and interpret a linear function in a scientific context.
3,212
mathematics
algebra
linear_relation
2
worked_example
Evaluate linear function y = -1.784 x + -11.58 at x = 9.18
The linear relation y = m x + b with slope m = -1.784 and intercept b = -11.58 evaluated at x = 9.18 yields y = -27.95. Linear models appear throughout science whenever a rate of change is approximately constant.
y = m x + b
basic arithmetic
Evaluate and interpret a linear function in a scientific context.
3,213
mathematics
algebra
linear_relation
2
worked_example
Evaluate linear function y = -1.715 x + 16.56 at x = -7.325
The linear relation y = m x + b with slope m = -1.715 and intercept b = 16.56 evaluated at x = -7.325 yields y = 29.13. Linear models appear throughout science whenever a rate of change is approximately constant.
y = m x + b
basic arithmetic
Evaluate and interpret a linear function in a scientific context.
3,214
mathematics
algebra
linear_relation
2
worked_example
Evaluate linear function y = 4.223 x + 4.351 at x = -9.914
The linear relation y = m x + b with slope m = 4.223 and intercept b = 4.351 evaluated at x = -9.914 yields y = -37.51. Linear models appear throughout science whenever a rate of change is approximately constant.
y = m x + b
basic arithmetic
Evaluate and interpret a linear function in a scientific context.
3,215
mathematics
algebra
linear_relation
2
worked_example
Evaluate linear function y = -4.904 x + -13.06 at x = 1.116
The linear relation y = m x + b with slope m = -4.904 and intercept b = -13.06 evaluated at x = 1.116 yields y = -18.53. Linear models appear throughout science whenever a rate of change is approximately constant.
y = m x + b
basic arithmetic
Evaluate and interpret a linear function in a scientific context.
3,216
mathematics
algebra
linear_relation
2
worked_example
Evaluate linear function y = 1.965 x + -0.4409 at x = -2.144
The linear relation y = m x + b with slope m = 1.965 and intercept b = -0.4409 evaluated at x = -2.144 yields y = -4.654. Linear models appear throughout science whenever a rate of change is approximately constant.
y = m x + b
basic arithmetic
Evaluate and interpret a linear function in a scientific context.
3,217
mathematics
algebra
linear_relation
2
worked_example
Evaluate linear function y = -4.189 x + 15.07 at x = 3.025
The linear relation y = m x + b with slope m = -4.189 and intercept b = 15.07 evaluated at x = 3.025 yields y = 2.397. Linear models appear throughout science whenever a rate of change is approximately constant.
y = m x + b
basic arithmetic
Evaluate and interpret a linear function in a scientific context.
3,218
mathematics
algebra
linear_relation
2
worked_example
Evaluate linear function y = 0.3865 x + 15.7 at x = 6.321
The linear relation y = m x + b with slope m = 0.3865 and intercept b = 15.7 evaluated at x = 6.321 yields y = 18.15. Linear models appear throughout science whenever a rate of change is approximately constant.
y = m x + b
basic arithmetic
Evaluate and interpret a linear function in a scientific context.
3,219
mathematics
algebra
linear_relation
2
worked_example
Evaluate linear function y = -0.5482 x + -15.06 at x = 9.441
The linear relation y = m x + b with slope m = -0.5482 and intercept b = -15.06 evaluated at x = 9.441 yields y = -20.24. Linear models appear throughout science whenever a rate of change is approximately constant.
y = m x + b
basic arithmetic
Evaluate and interpret a linear function in a scientific context.
3,220
mathematics
algebra
linear_relation
2
worked_example
Evaluate linear function y = -1.236 x + 4.052 at x = -2.265
The linear relation y = m x + b with slope m = -1.236 and intercept b = 4.052 evaluated at x = -2.265 yields y = 6.852. Linear models appear throughout science whenever a rate of change is approximately constant.
y = m x + b
basic arithmetic
Evaluate and interpret a linear function in a scientific context.
3,221
mathematics
algebra
linear_relation
2
worked_example
Evaluate linear function y = 3.391 x + 12.47 at x = 9.676
The linear relation y = m x + b with slope m = 3.391 and intercept b = 12.47 evaluated at x = 9.676 yields y = 45.29. Linear models appear throughout science whenever a rate of change is approximately constant.
y = m x + b
basic arithmetic
Evaluate and interpret a linear function in a scientific context.
3,222
mathematics
algebra
linear_relation
2
worked_example
Evaluate linear function y = -3.752 x + -5.181 at x = -6.14
The linear relation y = m x + b with slope m = -3.752 and intercept b = -5.181 evaluated at x = -6.14 yields y = 17.86. Linear models appear throughout science whenever a rate of change is approximately constant.
y = m x + b
basic arithmetic
Evaluate and interpret a linear function in a scientific context.
3,223
mathematics
algebra
linear_relation
2
worked_example
Evaluate linear function y = -4.906 x + 9.726 at x = 5.168
The linear relation y = m x + b with slope m = -4.906 and intercept b = 9.726 evaluated at x = 5.168 yields y = -15.63. Linear models appear throughout science whenever a rate of change is approximately constant.
y = m x + b
basic arithmetic
Evaluate and interpret a linear function in a scientific context.
3,224
mathematics
algebra
linear_relation
2
worked_example
Evaluate linear function y = 1.806 x + 8.368 at x = -6.17
The linear relation y = m x + b with slope m = 1.806 and intercept b = 8.368 evaluated at x = -6.17 yields y = -2.772. Linear models appear throughout science whenever a rate of change is approximately constant.
y = m x + b
basic arithmetic
Evaluate and interpret a linear function in a scientific context.
3,225
mathematics
algebra
linear_relation
2
worked_example
Evaluate linear function y = 3.163 x + 5.009 at x = 6.168
The linear relation y = m x + b with slope m = 3.163 and intercept b = 5.009 evaluated at x = 6.168 yields y = 24.52. Linear models appear throughout science whenever a rate of change is approximately constant.
y = m x + b
basic arithmetic
Evaluate and interpret a linear function in a scientific context.
3,226
mathematics
algebra
linear_relation
2
worked_example
Evaluate linear function y = -2.789 x + 19.2 at x = 9.346
The linear relation y = m x + b with slope m = -2.789 and intercept b = 19.2 evaluated at x = 9.346 yields y = -6.857. Linear models appear throughout science whenever a rate of change is approximately constant.
y = m x + b
basic arithmetic
Evaluate and interpret a linear function in a scientific context.
3,227
mathematics
algebra
linear_relation
2
worked_example
Evaluate linear function y = -4.632 x + -0.2865 at x = 4.081
The linear relation y = m x + b with slope m = -4.632 and intercept b = -0.2865 evaluated at x = 4.081 yields y = -19.19. Linear models appear throughout science whenever a rate of change is approximately constant.
y = m x + b
basic arithmetic
Evaluate and interpret a linear function in a scientific context.
3,228
mathematics
algebra
linear_relation
2
worked_example
Evaluate linear function y = 1.06 x + -19.71 at x = 9.685
The linear relation y = m x + b with slope m = 1.06 and intercept b = -19.71 evaluated at x = 9.685 yields y = -9.446. Linear models appear throughout science whenever a rate of change is approximately constant.
y = m x + b
basic arithmetic
Evaluate and interpret a linear function in a scientific context.
3,229
mathematics
algebra
linear_relation
2
worked_example
Evaluate linear function y = 1.384 x + -15.56 at x = -4.453
The linear relation y = m x + b with slope m = 1.384 and intercept b = -15.56 evaluated at x = -4.453 yields y = -21.73. Linear models appear throughout science whenever a rate of change is approximately constant.
y = m x + b
basic arithmetic
Evaluate and interpret a linear function in a scientific context.
3,230
mathematics
algebra
linear_relation
2
worked_example
Evaluate linear function y = 0.003256 x + -13.18 at x = -6.125
The linear relation y = m x + b with slope m = 0.003256 and intercept b = -13.18 evaluated at x = -6.125 yields y = -13.2. Linear models appear throughout science whenever a rate of change is approximately constant.
y = m x + b
basic arithmetic
Evaluate and interpret a linear function in a scientific context.
3,231
mathematics
algebra
linear_relation
2
worked_example
Evaluate linear function y = 2.388 x + 6.887 at x = 2.059
The linear relation y = m x + b with slope m = 2.388 and intercept b = 6.887 evaluated at x = 2.059 yields y = 11.81. Linear models appear throughout science whenever a rate of change is approximately constant.
y = m x + b
basic arithmetic
Evaluate and interpret a linear function in a scientific context.
3,232
mathematics
algebra
linear_relation
2
worked_example
Evaluate linear function y = -3.245 x + 3.527 at x = 4.919
The linear relation y = m x + b with slope m = -3.245 and intercept b = 3.527 evaluated at x = 4.919 yields y = -12.44. Linear models appear throughout science whenever a rate of change is approximately constant.
y = m x + b
basic arithmetic
Evaluate and interpret a linear function in a scientific context.
3,233
mathematics
algebra
linear_relation
2
worked_example
Evaluate linear function y = -3.726 x + 17.34 at x = 7.11
The linear relation y = m x + b with slope m = -3.726 and intercept b = 17.34 evaluated at x = 7.11 yields y = -9.146. Linear models appear throughout science whenever a rate of change is approximately constant.
y = m x + b
basic arithmetic
Evaluate and interpret a linear function in a scientific context.
3,234
mathematics
algebra
linear_relation
2
worked_example
Evaluate linear function y = 3.81 x + 9.156 at x = -4.513
The linear relation y = m x + b with slope m = 3.81 and intercept b = 9.156 evaluated at x = -4.513 yields y = -8.04. Linear models appear throughout science whenever a rate of change is approximately constant.
y = m x + b
basic arithmetic
Evaluate and interpret a linear function in a scientific context.
3,235
mathematics
algebra
linear_relation
2
worked_example
Evaluate linear function y = 3.477 x + -19.08 at x = 9.396
The linear relation y = m x + b with slope m = 3.477 and intercept b = -19.08 evaluated at x = 9.396 yields y = 13.59. Linear models appear throughout science whenever a rate of change is approximately constant.
y = m x + b
basic arithmetic
Evaluate and interpret a linear function in a scientific context.
3,236
mathematics
algebra
linear_relation
2
worked_example
Evaluate linear function y = 1.777 x + 4.578 at x = 3.614
The linear relation y = m x + b with slope m = 1.777 and intercept b = 4.578 evaluated at x = 3.614 yields y = 11. Linear models appear throughout science whenever a rate of change is approximately constant.
y = m x + b
basic arithmetic
Evaluate and interpret a linear function in a scientific context.
3,237
mathematics
algebra
linear_relation
2
worked_example
Evaluate linear function y = 3.831 x + -19.92 at x = -1.458
The linear relation y = m x + b with slope m = 3.831 and intercept b = -19.92 evaluated at x = -1.458 yields y = -25.51. Linear models appear throughout science whenever a rate of change is approximately constant.
y = m x + b
basic arithmetic
Evaluate and interpret a linear function in a scientific context.
3,238
mathematics
algebra
linear_relation
2
worked_example
Evaluate linear function y = 1.731 x + 6.001 at x = 7.077
The linear relation y = m x + b with slope m = 1.731 and intercept b = 6.001 evaluated at x = 7.077 yields y = 18.25. Linear models appear throughout science whenever a rate of change is approximately constant.
y = m x + b
basic arithmetic
Evaluate and interpret a linear function in a scientific context.
3,239
mathematics
algebra
linear_relation
2
worked_example
Evaluate linear function y = -1.77 x + 13.77 at x = -1.862
The linear relation y = m x + b with slope m = -1.77 and intercept b = 13.77 evaluated at x = -1.862 yields y = 17.07. Linear models appear throughout science whenever a rate of change is approximately constant.
y = m x + b
basic arithmetic
Evaluate and interpret a linear function in a scientific context.
3,240
mathematics
algebra
linear_relation
2
worked_example
Evaluate linear function y = -3.783 x + 0.7318 at x = -0.08851
The linear relation y = m x + b with slope m = -3.783 and intercept b = 0.7318 evaluated at x = -0.08851 yields y = 1.067. Linear models appear throughout science whenever a rate of change is approximately constant.
y = m x + b
basic arithmetic
Evaluate and interpret a linear function in a scientific context.
3,241
mathematics
algebra
linear_relation
2
worked_example
Evaluate linear function y = 0.1726 x + -18.26 at x = 4.424
The linear relation y = m x + b with slope m = 0.1726 and intercept b = -18.26 evaluated at x = 4.424 yields y = -17.5. Linear models appear throughout science whenever a rate of change is approximately constant.
y = m x + b
basic arithmetic
Evaluate and interpret a linear function in a scientific context.
3,242
mathematics
algebra
linear_relation
2
worked_example
Evaluate linear function y = -4.53 x + 16.74 at x = 0.6482
The linear relation y = m x + b with slope m = -4.53 and intercept b = 16.74 evaluated at x = 0.6482 yields y = 13.8. Linear models appear throughout science whenever a rate of change is approximately constant.
y = m x + b
basic arithmetic
Evaluate and interpret a linear function in a scientific context.
3,243
mathematics
algebra
linear_relation
2
worked_example
Evaluate linear function y = -1.838 x + -4.326 at x = -3.306
The linear relation y = m x + b with slope m = -1.838 and intercept b = -4.326 evaluated at x = -3.306 yields y = 1.749. Linear models appear throughout science whenever a rate of change is approximately constant.
y = m x + b
basic arithmetic
Evaluate and interpret a linear function in a scientific context.
3,244
mathematics
algebra
linear_relation
2
worked_example
Evaluate linear function y = 3.801 x + 12.31 at x = 9.805
The linear relation y = m x + b with slope m = 3.801 and intercept b = 12.31 evaluated at x = 9.805 yields y = 49.58. Linear models appear throughout science whenever a rate of change is approximately constant.
y = m x + b
basic arithmetic
Evaluate and interpret a linear function in a scientific context.
3,245
mathematics
algebra
linear_relation
2
worked_example
Evaluate linear function y = -2.744 x + 7.582 at x = 9.156
The linear relation y = m x + b with slope m = -2.744 and intercept b = 7.582 evaluated at x = 9.156 yields y = -17.54. Linear models appear throughout science whenever a rate of change is approximately constant.
y = m x + b
basic arithmetic
Evaluate and interpret a linear function in a scientific context.
3,246
mathematics
algebra
linear_relation
2
worked_example
Evaluate linear function y = 4.17 x + -12.12 at x = -3.416
The linear relation y = m x + b with slope m = 4.17 and intercept b = -12.12 evaluated at x = -3.416 yields y = -26.37. Linear models appear throughout science whenever a rate of change is approximately constant.
y = m x + b
basic arithmetic
Evaluate and interpret a linear function in a scientific context.
3,247
mathematics
algebra
linear_relation
2
worked_example
Evaluate linear function y = -4.372 x + 5.012 at x = -9.443
The linear relation y = m x + b with slope m = -4.372 and intercept b = 5.012 evaluated at x = -9.443 yields y = 46.29. Linear models appear throughout science whenever a rate of change is approximately constant.
y = m x + b
basic arithmetic
Evaluate and interpret a linear function in a scientific context.
3,248
mathematics
algebra
linear_relation
2
worked_example
Evaluate linear function y = -0.6805 x + -19.04 at x = 5.944
The linear relation y = m x + b with slope m = -0.6805 and intercept b = -19.04 evaluated at x = 5.944 yields y = -23.08. Linear models appear throughout science whenever a rate of change is approximately constant.
y = m x + b
basic arithmetic
Evaluate and interpret a linear function in a scientific context.
3,249
mathematics
algebra
linear_relation
2
worked_example
Evaluate linear function y = 4.351 x + 13.62 at x = -5.057
The linear relation y = m x + b with slope m = 4.351 and intercept b = 13.62 evaluated at x = -5.057 yields y = -8.38. Linear models appear throughout science whenever a rate of change is approximately constant.
y = m x + b
basic arithmetic
Evaluate and interpret a linear function in a scientific context.
3,250
mathematics
algebra
linear_relation
2
worked_example
Evaluate linear function y = -0.2642 x + 18.35 at x = 6.65
The linear relation y = m x + b with slope m = -0.2642 and intercept b = 18.35 evaluated at x = 6.65 yields y = 16.59. Linear models appear throughout science whenever a rate of change is approximately constant.
y = m x + b
basic arithmetic
Evaluate and interpret a linear function in a scientific context.
3,251
mathematics
algebra
linear_relation
2
worked_example
Evaluate linear function y = 3.216 x + 0.787 at x = -5.265
The linear relation y = m x + b with slope m = 3.216 and intercept b = 0.787 evaluated at x = -5.265 yields y = -16.15. Linear models appear throughout science whenever a rate of change is approximately constant.
y = m x + b
basic arithmetic
Evaluate and interpret a linear function in a scientific context.
3,252
mathematics
algebra
linear_relation
2
worked_example
Evaluate linear function y = -4.271 x + 3.999 at x = -1.229
The linear relation y = m x + b with slope m = -4.271 and intercept b = 3.999 evaluated at x = -1.229 yields y = 9.249. Linear models appear throughout science whenever a rate of change is approximately constant.
y = m x + b
basic arithmetic
Evaluate and interpret a linear function in a scientific context.
3,253
mathematics
algebra
linear_relation
2
worked_example
Evaluate linear function y = -4.043 x + -2.142 at x = -7.503
The linear relation y = m x + b with slope m = -4.043 and intercept b = -2.142 evaluated at x = -7.503 yields y = 28.2. Linear models appear throughout science whenever a rate of change is approximately constant.
y = m x + b
basic arithmetic
Evaluate and interpret a linear function in a scientific context.
3,254
mathematics
algebra
linear_relation
2
worked_example
Evaluate linear function y = 4.745 x + 16.67 at x = -2.452
The linear relation y = m x + b with slope m = 4.745 and intercept b = 16.67 evaluated at x = -2.452 yields y = 5.033. Linear models appear throughout science whenever a rate of change is approximately constant.
y = m x + b
basic arithmetic
Evaluate and interpret a linear function in a scientific context.
3,255
mathematics
algebra
linear_relation
2
worked_example
Evaluate linear function y = 3.901 x + 7.735 at x = 5.653
The linear relation y = m x + b with slope m = 3.901 and intercept b = 7.735 evaluated at x = 5.653 yields y = 29.79. Linear models appear throughout science whenever a rate of change is approximately constant.
y = m x + b
basic arithmetic
Evaluate and interpret a linear function in a scientific context.
3,256
mathematics
algebra
linear_relation
2
worked_example
Evaluate linear function y = -4.38 x + 12.1 at x = -8.904
The linear relation y = m x + b with slope m = -4.38 and intercept b = 12.1 evaluated at x = -8.904 yields y = 51.1. Linear models appear throughout science whenever a rate of change is approximately constant.
y = m x + b
basic arithmetic
Evaluate and interpret a linear function in a scientific context.
3,257
mathematics
algebra
linear_relation
2
worked_example
Evaluate linear function y = 1.107 x + -2.726 at x = -7.963
The linear relation y = m x + b with slope m = 1.107 and intercept b = -2.726 evaluated at x = -7.963 yields y = -11.55. Linear models appear throughout science whenever a rate of change is approximately constant.
y = m x + b
basic arithmetic
Evaluate and interpret a linear function in a scientific context.
3,258
mathematics
algebra
linear_relation
2
worked_example
Evaluate linear function y = -4.442 x + -17.91 at x = 6.999
The linear relation y = m x + b with slope m = -4.442 and intercept b = -17.91 evaluated at x = 6.999 yields y = -49. Linear models appear throughout science whenever a rate of change is approximately constant.
y = m x + b
basic arithmetic
Evaluate and interpret a linear function in a scientific context.
3,259
mathematics
algebra
linear_relation
2
worked_example
Evaluate linear function y = -0.9832 x + 4.692 at x = -1.778
The linear relation y = m x + b with slope m = -0.9832 and intercept b = 4.692 evaluated at x = -1.778 yields y = 6.44. Linear models appear throughout science whenever a rate of change is approximately constant.
y = m x + b
basic arithmetic
Evaluate and interpret a linear function in a scientific context.
3,260
mathematics
algebra
linear_relation
2
worked_example
Evaluate linear function y = 3.646 x + 11.5 at x = 2.48
The linear relation y = m x + b with slope m = 3.646 and intercept b = 11.5 evaluated at x = 2.48 yields y = 20.54. Linear models appear throughout science whenever a rate of change is approximately constant.
y = m x + b
basic arithmetic
Evaluate and interpret a linear function in a scientific context.
3,261
mathematics
algebra
linear_relation
2
worked_example
Evaluate linear function y = -0.4659 x + -1.432 at x = -1.438
The linear relation y = m x + b with slope m = -0.4659 and intercept b = -1.432 evaluated at x = -1.438 yields y = -0.7617. Linear models appear throughout science whenever a rate of change is approximately constant.
y = m x + b
basic arithmetic
Evaluate and interpret a linear function in a scientific context.
3,262
mathematics
algebra
linear_relation
2
worked_example
Evaluate linear function y = 1.202 x + -15.95 at x = 3.018
The linear relation y = m x + b with slope m = 1.202 and intercept b = -15.95 evaluated at x = 3.018 yields y = -12.32. Linear models appear throughout science whenever a rate of change is approximately constant.
y = m x + b
basic arithmetic
Evaluate and interpret a linear function in a scientific context.
3,263
mathematics
algebra
linear_relation
2
worked_example
Evaluate linear function y = 1.758 x + -18.96 at x = 0.3443
The linear relation y = m x + b with slope m = 1.758 and intercept b = -18.96 evaluated at x = 0.3443 yields y = -18.36. Linear models appear throughout science whenever a rate of change is approximately constant.
y = m x + b
basic arithmetic
Evaluate and interpret a linear function in a scientific context.
3,264
mathematics
algebra
linear_relation
2
worked_example
Evaluate linear function y = 0.8781 x + -15.68 at x = -9.754
The linear relation y = m x + b with slope m = 0.8781 and intercept b = -15.68 evaluated at x = -9.754 yields y = -24.25. Linear models appear throughout science whenever a rate of change is approximately constant.
y = m x + b
basic arithmetic
Evaluate and interpret a linear function in a scientific context.
3,265
mathematics
algebra
linear_relation
2
worked_example
Evaluate linear function y = 2.133 x + 3.715 at x = 6.816
The linear relation y = m x + b with slope m = 2.133 and intercept b = 3.715 evaluated at x = 6.816 yields y = 18.25. Linear models appear throughout science whenever a rate of change is approximately constant.
y = m x + b
basic arithmetic
Evaluate and interpret a linear function in a scientific context.
3,266
mathematics
algebra
linear_relation
2
worked_example
Evaluate linear function y = 4.044 x + -14.96 at x = 0.178
The linear relation y = m x + b with slope m = 4.044 and intercept b = -14.96 evaluated at x = 0.178 yields y = -14.24. Linear models appear throughout science whenever a rate of change is approximately constant.
y = m x + b
basic arithmetic
Evaluate and interpret a linear function in a scientific context.
3,267
mathematics
algebra
linear_relation
2
worked_example
Evaluate linear function y = -1.446 x + -0.744 at x = 2.417
The linear relation y = m x + b with slope m = -1.446 and intercept b = -0.744 evaluated at x = 2.417 yields y = -4.239. Linear models appear throughout science whenever a rate of change is approximately constant.
y = m x + b
basic arithmetic
Evaluate and interpret a linear function in a scientific context.
3,268
mathematics
algebra
linear_relation
2
worked_example
Evaluate linear function y = -3.141 x + -14.49 at x = -9.119
The linear relation y = m x + b with slope m = -3.141 and intercept b = -14.49 evaluated at x = -9.119 yields y = 14.15. Linear models appear throughout science whenever a rate of change is approximately constant.
y = m x + b
basic arithmetic
Evaluate and interpret a linear function in a scientific context.
3,269
mathematics
algebra
linear_relation
2
worked_example
Evaluate linear function y = -3.723 x + 3.381 at x = 0.2625
The linear relation y = m x + b with slope m = -3.723 and intercept b = 3.381 evaluated at x = 0.2625 yields y = 2.403. Linear models appear throughout science whenever a rate of change is approximately constant.
y = m x + b
basic arithmetic
Evaluate and interpret a linear function in a scientific context.
3,270
mathematics
algebra
linear_relation
2
worked_example
Evaluate linear function y = 1.517 x + -5.69 at x = 1.673
The linear relation y = m x + b with slope m = 1.517 and intercept b = -5.69 evaluated at x = 1.673 yields y = -3.152. Linear models appear throughout science whenever a rate of change is approximately constant.
y = m x + b
basic arithmetic
Evaluate and interpret a linear function in a scientific context.
3,271
mathematics
algebra
linear_relation
2
worked_example
Evaluate linear function y = 0.4114 x + -14.18 at x = -0.6095
The linear relation y = m x + b with slope m = 0.4114 and intercept b = -14.18 evaluated at x = -0.6095 yields y = -14.43. Linear models appear throughout science whenever a rate of change is approximately constant.
y = m x + b
basic arithmetic
Evaluate and interpret a linear function in a scientific context.
3,272
mathematics
algebra
linear_relation
2
worked_example
Evaluate linear function y = 1.033 x + -8.357 at x = 9.405
The linear relation y = m x + b with slope m = 1.033 and intercept b = -8.357 evaluated at x = 9.405 yields y = 1.361. Linear models appear throughout science whenever a rate of change is approximately constant.
y = m x + b
basic arithmetic
Evaluate and interpret a linear function in a scientific context.
3,273
mathematics
algebra
linear_relation
2
worked_example
Evaluate linear function y = 0.1768 x + 6.307 at x = -7.108
The linear relation y = m x + b with slope m = 0.1768 and intercept b = 6.307 evaluated at x = -7.108 yields y = 5.05. Linear models appear throughout science whenever a rate of change is approximately constant.
y = m x + b
basic arithmetic
Evaluate and interpret a linear function in a scientific context.
3,274
mathematics
algebra
linear_relation
2
worked_example
Evaluate linear function y = -2.626 x + 12.77 at x = 1.189
The linear relation y = m x + b with slope m = -2.626 and intercept b = 12.77 evaluated at x = 1.189 yields y = 9.645. Linear models appear throughout science whenever a rate of change is approximately constant.
y = m x + b
basic arithmetic
Evaluate and interpret a linear function in a scientific context.
3,275
mathematics
algebra
linear_relation
2
worked_example
Evaluate linear function y = -4.454 x + -6.247 at x = 9.53
The linear relation y = m x + b with slope m = -4.454 and intercept b = -6.247 evaluated at x = 9.53 yields y = -48.69. Linear models appear throughout science whenever a rate of change is approximately constant.
y = m x + b
basic arithmetic
Evaluate and interpret a linear function in a scientific context.
3,276
mathematics
algebra
linear_relation
2
worked_example
Evaluate linear function y = 1.406 x + -11.95 at x = -8.632
The linear relation y = m x + b with slope m = 1.406 and intercept b = -11.95 evaluated at x = -8.632 yields y = -24.08. Linear models appear throughout science whenever a rate of change is approximately constant.
y = m x + b
basic arithmetic
Evaluate and interpret a linear function in a scientific context.
3,277
mathematics
algebra
linear_relation
2
worked_example
Evaluate linear function y = -3.106 x + -0.971 at x = 3.837
The linear relation y = m x + b with slope m = -3.106 and intercept b = -0.971 evaluated at x = 3.837 yields y = -12.89. Linear models appear throughout science whenever a rate of change is approximately constant.
y = m x + b
basic arithmetic
Evaluate and interpret a linear function in a scientific context.
3,278
mathematics
algebra
linear_relation
2
worked_example
Evaluate linear function y = -0.326 x + 7.697 at x = 7.04
The linear relation y = m x + b with slope m = -0.326 and intercept b = 7.697 evaluated at x = 7.04 yields y = 5.402. Linear models appear throughout science whenever a rate of change is approximately constant.
y = m x + b
basic arithmetic
Evaluate and interpret a linear function in a scientific context.
3,279
mathematics
algebra
linear_relation
2
worked_example
Evaluate linear function y = 0.661 x + -6.574 at x = -4.007
The linear relation y = m x + b with slope m = 0.661 and intercept b = -6.574 evaluated at x = -4.007 yields y = -9.222. Linear models appear throughout science whenever a rate of change is approximately constant.
y = m x + b
basic arithmetic
Evaluate and interpret a linear function in a scientific context.
3,280
mathematics
algebra
linear_relation
2
worked_example
Evaluate linear function y = -1.714 x + -15.81 at x = 7.522
The linear relation y = m x + b with slope m = -1.714 and intercept b = -15.81 evaluated at x = 7.522 yields y = -28.7. Linear models appear throughout science whenever a rate of change is approximately constant.
y = m x + b
basic arithmetic
Evaluate and interpret a linear function in a scientific context.
3,281
mathematics
algebra
linear_relation
2
worked_example
Evaluate linear function y = 4.105 x + -0.1628 at x = 8.399
The linear relation y = m x + b with slope m = 4.105 and intercept b = -0.1628 evaluated at x = 8.399 yields y = 34.32. Linear models appear throughout science whenever a rate of change is approximately constant.
y = m x + b
basic arithmetic
Evaluate and interpret a linear function in a scientific context.
3,282
mathematics
algebra
linear_relation
2
worked_example
Evaluate linear function y = 1.388 x + 7.729 at x = -0.6693
The linear relation y = m x + b with slope m = 1.388 and intercept b = 7.729 evaluated at x = -0.6693 yields y = 6.8. Linear models appear throughout science whenever a rate of change is approximately constant.
y = m x + b
basic arithmetic
Evaluate and interpret a linear function in a scientific context.
3,283
mathematics
algebra
linear_relation
2
worked_example
Evaluate linear function y = -2.869 x + -0.7702 at x = 5.367
The linear relation y = m x + b with slope m = -2.869 and intercept b = -0.7702 evaluated at x = 5.367 yields y = -16.17. Linear models appear throughout science whenever a rate of change is approximately constant.
y = m x + b
basic arithmetic
Evaluate and interpret a linear function in a scientific context.
3,284
mathematics
algebra
linear_relation
2
worked_example
Evaluate linear function y = 3.147 x + 12.29 at x = -2.482
The linear relation y = m x + b with slope m = 3.147 and intercept b = 12.29 evaluated at x = -2.482 yields y = 4.482. Linear models appear throughout science whenever a rate of change is approximately constant.
y = m x + b
basic arithmetic
Evaluate and interpret a linear function in a scientific context.
3,285
mathematics
logarithms
common_logarithm
3
worked_example
Common logarithm of 0.06364
The common logarithm log₁₀(0.06364) = -1.196. Logarithms convert multiplicative relationships into additive ones and are indispensable for expressing quantities that span many orders of magnitude (pH, sound intensity, stellar magnitudes, earthquake energy).
log10(x)
exponents
Compute and interpret common logarithms of scientific quantities.
3,286
mathematics
logarithms
common_logarithm
3
worked_example
Common logarithm of 8185
The common logarithm log₁₀(8185) = 3.913. Logarithms convert multiplicative relationships into additive ones and are indispensable for expressing quantities that span many orders of magnitude (pH, sound intensity, stellar magnitudes, earthquake energy).
log10(x)
exponents
Compute and interpret common logarithms of scientific quantities.
3,287
mathematics
logarithms
common_logarithm
3
worked_example
Common logarithm of 1.2042e-06
The common logarithm log₁₀(1.2042e-06) = -5.919. Logarithms convert multiplicative relationships into additive ones and are indispensable for expressing quantities that span many orders of magnitude (pH, sound intensity, stellar magnitudes, earthquake energy).
log10(x)
exponents
Compute and interpret common logarithms of scientific quantities.
3,288
mathematics
logarithms
common_logarithm
3
worked_example
Common logarithm of 1.3143e-06
The common logarithm log₁₀(1.3143e-06) = -5.881. Logarithms convert multiplicative relationships into additive ones and are indispensable for expressing quantities that span many orders of magnitude (pH, sound intensity, stellar magnitudes, earthquake energy).
log10(x)
exponents
Compute and interpret common logarithms of scientific quantities.
3,289
mathematics
logarithms
common_logarithm
3
worked_example
Common logarithm of 0.01971
The common logarithm log₁₀(0.01971) = -1.705. Logarithms convert multiplicative relationships into additive ones and are indispensable for expressing quantities that span many orders of magnitude (pH, sound intensity, stellar magnitudes, earthquake energy).
log10(x)
exponents
Compute and interpret common logarithms of scientific quantities.
3,290
mathematics
logarithms
common_logarithm
3
worked_example
Common logarithm of 4.532
The common logarithm log₁₀(4.532) = 0.6563. Logarithms convert multiplicative relationships into additive ones and are indispensable for expressing quantities that span many orders of magnitude (pH, sound intensity, stellar magnitudes, earthquake energy).
log10(x)
exponents
Compute and interpret common logarithms of scientific quantities.
3,291
mathematics
logarithms
common_logarithm
3
worked_example
Common logarithm of 5.1147e-05
The common logarithm log₁₀(5.1147e-05) = -4.291. Logarithms convert multiplicative relationships into additive ones and are indispensable for expressing quantities that span many orders of magnitude (pH, sound intensity, stellar magnitudes, earthquake energy).
log10(x)
exponents
Compute and interpret common logarithms of scientific quantities.
3,292
mathematics
logarithms
common_logarithm
3
worked_example
Common logarithm of 0.1927
The common logarithm log₁₀(0.1927) = -0.7151. Logarithms convert multiplicative relationships into additive ones and are indispensable for expressing quantities that span many orders of magnitude (pH, sound intensity, stellar magnitudes, earthquake energy).
log10(x)
exponents
Compute and interpret common logarithms of scientific quantities.
3,293
mathematics
logarithms
common_logarithm
3
worked_example
Common logarithm of 37.67
The common logarithm log₁₀(37.67) = 1.576. Logarithms convert multiplicative relationships into additive ones and are indispensable for expressing quantities that span many orders of magnitude (pH, sound intensity, stellar magnitudes, earthquake energy).
log10(x)
exponents
Compute and interpret common logarithms of scientific quantities.
3,294
mathematics
logarithms
common_logarithm
3
worked_example
Common logarithm of 8.9641e+04
The common logarithm log₁₀(8.9641e+04) = 4.953. Logarithms convert multiplicative relationships into additive ones and are indispensable for expressing quantities that span many orders of magnitude (pH, sound intensity, stellar magnitudes, earthquake energy).
log10(x)
exponents
Compute and interpret common logarithms of scientific quantities.
3,295
mathematics
logarithms
common_logarithm
3
worked_example
Common logarithm of 0.02084
The common logarithm log₁₀(0.02084) = -1.681. Logarithms convert multiplicative relationships into additive ones and are indispensable for expressing quantities that span many orders of magnitude (pH, sound intensity, stellar magnitudes, earthquake energy).
log10(x)
exponents
Compute and interpret common logarithms of scientific quantities.
3,296
mathematics
logarithms
common_logarithm
3
worked_example
Common logarithm of 5.0549e+05
The common logarithm log₁₀(5.0549e+05) = 5.704. Logarithms convert multiplicative relationships into additive ones and are indispensable for expressing quantities that span many orders of magnitude (pH, sound intensity, stellar magnitudes, earthquake energy).
log10(x)
exponents
Compute and interpret common logarithms of scientific quantities.
3,297
mathematics
logarithms
common_logarithm
3
worked_example
Common logarithm of 2.4517e-04
The common logarithm log₁₀(2.4517e-04) = -3.611. Logarithms convert multiplicative relationships into additive ones and are indispensable for expressing quantities that span many orders of magnitude (pH, sound intensity, stellar magnitudes, earthquake energy).
log10(x)
exponents
Compute and interpret common logarithms of scientific quantities.
3,298
mathematics
logarithms
common_logarithm
3
worked_example
Common logarithm of 0.002566
The common logarithm log₁₀(0.002566) = -2.591. Logarithms convert multiplicative relationships into additive ones and are indispensable for expressing quantities that span many orders of magnitude (pH, sound intensity, stellar magnitudes, earthquake energy).
log10(x)
exponents
Compute and interpret common logarithms of scientific quantities.
3,299
mathematics
logarithms
common_logarithm
3
worked_example
Common logarithm of 4.2398e-04
The common logarithm log₁₀(4.2398e-04) = -3.373. Logarithms convert multiplicative relationships into additive ones and are indispensable for expressing quantities that span many orders of magnitude (pH, sound intensity, stellar magnitudes, earthquake energy).
log10(x)
exponents
Compute and interpret common logarithms of scientific quantities.
3,300
mathematics
logarithms
common_logarithm
3
worked_example
Common logarithm of 0.001393
The common logarithm log₁₀(0.001393) = -2.856. Logarithms convert multiplicative relationships into additive ones and are indispensable for expressing quantities that span many orders of magnitude (pH, sound intensity, stellar magnitudes, earthquake energy).
log10(x)
exponents
Compute and interpret common logarithms of scientific quantities.