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Step 5.Solvethe equation using good algebra techniques. | https://openstax.org/books/elementary-algebra-2e/pages/3-key-concepts |
Step 6.Checkthe answer in the problem and make sure it makes sense. | https://openstax.org/books/elementary-algebra-2e/pages/3-key-concepts |
Step 7.Answerthe question with a complete sentence. | https://openstax.org/books/elementary-algebra-2e/pages/3-key-concepts |
Solving inequalitiesStep 1.Readthe problem.Step 2.Identifywhat we are looking for.Step 3.Namewhat we are looking for. Choose a variable to represent that quantity.Step 4.Translate.Write a sentence that gives the information to find it. Translate into an inequality.Step 5.Solvethe inequality.Step 6.Checkthe answer in th... | https://openstax.org/books/elementary-algebra-2e/pages/3-key-concepts |
Step 1.Readthe problem. | https://openstax.org/books/elementary-algebra-2e/pages/3-key-concepts |
Step 2.Identifywhat we are looking for. | https://openstax.org/books/elementary-algebra-2e/pages/3-key-concepts |
Step 3.Namewhat we are looking for. Choose a variable to represent that quantity. | https://openstax.org/books/elementary-algebra-2e/pages/3-key-concepts |
Step 4.Translate.Write a sentence that gives the information to find it. Translate into an inequality. | https://openstax.org/books/elementary-algebra-2e/pages/3-key-concepts |
Step 5.Solvethe inequality. | https://openstax.org/books/elementary-algebra-2e/pages/3-key-concepts |
Step 6.Checkthe answer in the problem and make sure it makes sense. | https://openstax.org/books/elementary-algebra-2e/pages/3-key-concepts |
Step 7.Answerthe question with a complete sentence. | https://openstax.org/books/elementary-algebra-2e/pages/3-key-concepts |
amount of discount : The amount of discount is the amount resulting when a discount rate is multiplied by the original price of an item. | https://openstax.org/books/elementary-algebra-2e/pages/3-key-terms |
discount rate : The discount rate is the percent used to determine the amount of a discount, common in retail settings. | https://openstax.org/books/elementary-algebra-2e/pages/3-key-terms |
interest : Interest is the money that a bank pays its customers for keeping their money in the bank. | https://openstax.org/books/elementary-algebra-2e/pages/3-key-terms |
list price : The list price is the price a retailer sells an item for. | https://openstax.org/books/elementary-algebra-2e/pages/3-key-terms |
mark-up : A mark-up is a percentage of the original cost used to increase the price of an item. | https://openstax.org/books/elementary-algebra-2e/pages/3-key-terms |
mixture problems : Mixture problems combine two or more items with different values together. | https://openstax.org/books/elementary-algebra-2e/pages/3-key-terms |
original cost : The original cost in a retail setting, is the price that a retailer pays for an item. | https://openstax.org/books/elementary-algebra-2e/pages/3-key-terms |
principal : The principal is the original amount of money invested or borrowed for a period of time at a specific interest rate. | https://openstax.org/books/elementary-algebra-2e/pages/3-key-terms |
rate of interest : The rate of interest is a percent of the principal, usually expressed as a percent per year. | https://openstax.org/books/elementary-algebra-2e/pages/3-key-terms |
simple interest : Simple interest is the interest earned according to the formulaI=Prt.I=Prt. | https://openstax.org/books/elementary-algebra-2e/pages/3-key-terms |
Sign Patterns of the QuadrantsQuadrant IQuadrant IIQuadrant IIIQuadrant IV(x,y)(x,y)(x,y)(x,y)(+,+)(â,+)(â,â)(+,â)Quadrant IQuadrant IIQuadrant IIIQuadrant IV(x,y)(x,y)(x,y)(x,y)(+,+)(â,+)(â,â)(+,â) | https://openstax.org/books/elementary-algebra-2e/pages/4-key-concepts |
Points on the AxesOn thex-axis,y=0y=0. Points with ay-coordinate equal to 0 are on thex-axis, and have coordinates(a,0)(a,0).On they-axis,x=0x=0. Points with anx-coordinate equal to 0 are on they-axis, and have coordinates(0,b).(0,b). | https://openstax.org/books/elementary-algebra-2e/pages/4-key-concepts |
On thex-axis,y=0y=0. Points with ay-coordinate equal to 0 are on thex-axis, and have coordinates(a,0)(a,0). | https://openstax.org/books/elementary-algebra-2e/pages/4-key-concepts |
On they-axis,x=0x=0. Points with anx-coordinate equal to 0 are on they-axis, and have coordinates(0,b).(0,b). | https://openstax.org/books/elementary-algebra-2e/pages/4-key-concepts |
Solution of a Linear EquationAn ordered pair(x,y)(x,y)is a solution of the linear equationAx+By=CAx+By=C, if the equation is a true statement when thex- andy- values of the ordered pair are substituted into the equation. | https://openstax.org/books/elementary-algebra-2e/pages/4-key-concepts |
An ordered pair(x,y)(x,y)is a solution of the linear equationAx+By=CAx+By=C, if the equation is a true statement when thex- andy- values of the ordered pair are substituted into the equation. | https://openstax.org/books/elementary-algebra-2e/pages/4-key-concepts |
Graph a Linear Equation by Plotting PointsStep 1.Find three points whose coordinates are solutions to the equation. Organize them in a table.Step 2.Plot the points in a rectangular coordinate system. Check that the points line up. If they do not, carefully check your work!Step 3.Draw the line through the three points. ... | https://openstax.org/books/elementary-algebra-2e/pages/4-key-concepts |
Step 1.Find three points whose coordinates are solutions to the equation. Organize them in a table. | https://openstax.org/books/elementary-algebra-2e/pages/4-key-concepts |
Step 2.Plot the points in a rectangular coordinate system. Check that the points line up. If they do not, carefully check your work! | https://openstax.org/books/elementary-algebra-2e/pages/4-key-concepts |
Step 3.Draw the line through the three points. Extend the line to fill the grid and put arrows on both ends of the line. | https://openstax.org/books/elementary-algebra-2e/pages/4-key-concepts |
Find thex- andy- Intercepts from the Equation of a LineUse the equation of the line to find thex- intercept of the line, lety=0y=0and solve forx.Use the equation of the line to find they- intercept of the line, letx=0x=0and solve fory. | https://openstax.org/books/elementary-algebra-2e/pages/4-key-concepts |
Use the equation of the line to find thex- intercept of the line, lety=0y=0and solve forx. | https://openstax.org/books/elementary-algebra-2e/pages/4-key-concepts |
Use the equation of the line to find they- intercept of the line, letx=0x=0and solve fory. | https://openstax.org/books/elementary-algebra-2e/pages/4-key-concepts |
Graph a Linear Equation using the InterceptsStep 1.Find thex- andy- intercepts of the line.Lety=0y=0and solve forx.Letx=0x=0and solve fory.Step 2.Find a third solution to the equation.Step 3.Plot the three points and then check that they line up.Step 4.Draw the line. | https://openstax.org/books/elementary-algebra-2e/pages/4-key-concepts |
Step 1.Find thex- andy- intercepts of the line.Lety=0y=0and solve forx.Letx=0x=0and solve fory. | https://openstax.org/books/elementary-algebra-2e/pages/4-key-concepts |
Step 2.Find a third solution to the equation. | https://openstax.org/books/elementary-algebra-2e/pages/4-key-concepts |
Step 3.Plot the three points and then check that they line up. | https://openstax.org/books/elementary-algebra-2e/pages/4-key-concepts |
Step 4.Draw the line. | https://openstax.org/books/elementary-algebra-2e/pages/4-key-concepts |
Strategy for Choosing the Most Convenient Method to Graph a Line:Consider the form of the equation.If it only has one variable, it is a vertical or horizontal line.x=ax=ais a vertical line passing through thex- axis ataay=by=bis a horizontal line passing through they- axis atbb.Ifyis isolated on one side of the equatio... | https://openstax.org/books/elementary-algebra-2e/pages/4-key-concepts |
Consider the form of the equation. | https://openstax.org/books/elementary-algebra-2e/pages/4-key-concepts |
If it only has one variable, it is a vertical or horizontal line.x=ax=ais a vertical line passing through thex- axis ataay=by=bis a horizontal line passing through they- axis atbb. | https://openstax.org/books/elementary-algebra-2e/pages/4-key-concepts |
Ifyis isolated on one side of the equation, graph by plotting points. | https://openstax.org/books/elementary-algebra-2e/pages/4-key-concepts |
Choose any three values forxand then solve for the correspondingy- values. | https://openstax.org/books/elementary-algebra-2e/pages/4-key-concepts |
If the equation is of the formax+by=cax+by=c, find the intercepts. Find thex- andy- intercepts and then a third point. | https://openstax.org/books/elementary-algebra-2e/pages/4-key-concepts |
Find the Slope of a Line from its Graph usingm=riserunm=riserunStep 1.Locate two points on the line whose coordinates are integers.Step 2.Starting with the point on the left, sketch a right triangle, going from the first point to the second point.Step 3.Count the rise and the run on the legs of the triangle.Step 4.Take... | https://openstax.org/books/elementary-algebra-2e/pages/4-key-concepts |
Step 1.Locate two points on the line whose coordinates are integers. | https://openstax.org/books/elementary-algebra-2e/pages/4-key-concepts |
Step 2.Starting with the point on the left, sketch a right triangle, going from the first point to the second point. | https://openstax.org/books/elementary-algebra-2e/pages/4-key-concepts |
Step 3.Count the rise and the run on the legs of the triangle. | https://openstax.org/books/elementary-algebra-2e/pages/4-key-concepts |
Step 4.Take the ratio of rise to run to find the slope. | https://openstax.org/books/elementary-algebra-2e/pages/4-key-concepts |
Graph a Line Given a Point and the SlopeStep 1.Plot the given point.Step 2.Use the slope formulam=riserunm=riserunto identify the rise and the run.Step 3.Starting at the given point, count out the rise and run to mark the second point.Step 4.Connect the points with a line. | https://openstax.org/books/elementary-algebra-2e/pages/4-key-concepts |
Step 1.Plot the given point. | https://openstax.org/books/elementary-algebra-2e/pages/4-key-concepts |
Step 2.Use the slope formulam=riserunm=riserunto identify the rise and the run. | https://openstax.org/books/elementary-algebra-2e/pages/4-key-concepts |
Step 3.Starting at the given point, count out the rise and run to mark the second point. | https://openstax.org/books/elementary-algebra-2e/pages/4-key-concepts |
Step 4.Connect the points with a line. | https://openstax.org/books/elementary-algebra-2e/pages/4-key-concepts |
Slope of a Horizontal LineThe slope of a horizontal line,y=by=b, is 0. | https://openstax.org/books/elementary-algebra-2e/pages/4-key-concepts |
The slope of a horizontal line,y=by=b, is 0. | https://openstax.org/books/elementary-algebra-2e/pages/4-key-concepts |
Slope of a vertical lineThe slope of a vertical line,x=ax=a, is undefined | https://openstax.org/books/elementary-algebra-2e/pages/4-key-concepts |
The slope of a vertical line,x=ax=a, is undefined | https://openstax.org/books/elementary-algebra-2e/pages/4-key-concepts |
The slopeâintercept form of an equation of a line with slopemmandy-intercept,(0,b)(0,b)is,y=mx+by=mx+b. | https://openstax.org/books/elementary-algebra-2e/pages/4-key-concepts |
Graph a Line Using its Slope andy-InterceptStep 1.Find the slope-intercept form of the equation of the line.Step 2.Identify the slope andy-intercept.Step 3.Plot they-intercept.Step 4.Use the slope formulam=riserunm=riserunto identify the rise and the run.Step 5.Starting at they-intercept, count out the rise and run to ... | https://openstax.org/books/elementary-algebra-2e/pages/4-key-concepts |
Step 1.Find the slope-intercept form of the equation of the line. | https://openstax.org/books/elementary-algebra-2e/pages/4-key-concepts |
Step 2.Identify the slope andy-intercept. | https://openstax.org/books/elementary-algebra-2e/pages/4-key-concepts |
Step 3.Plot they-intercept. | https://openstax.org/books/elementary-algebra-2e/pages/4-key-concepts |
Step 4.Use the slope formulam=riserunm=riserunto identify the rise and the run. | https://openstax.org/books/elementary-algebra-2e/pages/4-key-concepts |
Step 5.Starting at they-intercept, count out the rise and run to mark the second point. | https://openstax.org/books/elementary-algebra-2e/pages/4-key-concepts |
Step 6.Connect the points with a line. | https://openstax.org/books/elementary-algebra-2e/pages/4-key-concepts |
Strategy for Choosing the Most Convenient Method to Graph a Line:Consider the form of the equation.If it only has one variable, it is a vertical or horizontal line.x=ax=ais a vertical line passing through thex-axis ataa.y=by=bis a horizontal line passing through they-axis atbb.Ifyyis isolated on one side of the equatio... | https://openstax.org/books/elementary-algebra-2e/pages/4-key-concepts |
If it only has one variable, it is a vertical or horizontal line.x=ax=ais a vertical line passing through thex-axis ataa.y=by=bis a horizontal line passing through they-axis atbb. | https://openstax.org/books/elementary-algebra-2e/pages/4-key-concepts |
Ifyyis isolated on one side of the equation, in the formy=mx+by=mx+b, graph by using the slope andy-intercept.Identify the slope andy-intercept and then graph. | https://openstax.org/books/elementary-algebra-2e/pages/4-key-concepts |
If the equation is of the formAx+By=CAx+By=C, find the intercepts.Find thex- andy-intercepts, a third point, and then graph. | https://openstax.org/books/elementary-algebra-2e/pages/4-key-concepts |
Parallel lines are lines in the same plane that do not intersect.Parallel lines have the same slope and differenty-intercepts.Ifm1andm2are the slopes of two parallel lines thenm1=m2.m1=m2.Parallel vertical lines have differentx-intercepts. | https://openstax.org/books/elementary-algebra-2e/pages/4-key-concepts |
Parallel lines have the same slope and differenty-intercepts. | https://openstax.org/books/elementary-algebra-2e/pages/4-key-concepts |
Ifm1andm2are the slopes of two parallel lines thenm1=m2.m1=m2. | https://openstax.org/books/elementary-algebra-2e/pages/4-key-concepts |
Parallel vertical lines have differentx-intercepts. | https://openstax.org/books/elementary-algebra-2e/pages/4-key-concepts |
Perpendicular lines are lines in the same plane that form a right angle.Ifm1andm2m1andm2are the slopes of two perpendicular lines, thenm1·m2=â1m1·m2=â1andm1=â1m2m1=â1m2.Vertical lines and horizontal lines are always perpendicular to each other. | https://openstax.org/books/elementary-algebra-2e/pages/4-key-concepts |
Ifm1andm2m1andm2are the slopes of two perpendicular lines, thenm1·m2=â1m1·m2=â1andm1=â1m2m1=â1m2. | https://openstax.org/books/elementary-algebra-2e/pages/4-key-concepts |
Vertical lines and horizontal lines are always perpendicular to each other. | https://openstax.org/books/elementary-algebra-2e/pages/4-key-concepts |
To Find an Equation of a Line Given the Slope and a PointStep 1.Identify the slope.Step 2.Identify the point.Step 3.Substitute the values into the point-slope form,yây1=m(xâx1)yây1=m(xâx1).Step 4.Write the equation in slope-intercept form. | https://openstax.org/books/elementary-algebra-2e/pages/4-key-concepts |
Step 1.Identify the slope. | https://openstax.org/books/elementary-algebra-2e/pages/4-key-concepts |
Step 2.Identify the point. | https://openstax.org/books/elementary-algebra-2e/pages/4-key-concepts |
Step 3.Substitute the values into the point-slope form,yây1=m(xâx1)yây1=m(xâx1). | https://openstax.org/books/elementary-algebra-2e/pages/4-key-concepts |
Step 4.Write the equation in slope-intercept form. | https://openstax.org/books/elementary-algebra-2e/pages/4-key-concepts |
To Find an Equation of a Line Given Two PointsStep 1.Find the slope using the given points.Step 2.Choose one point.Step 3.Substitute the values into the point-slope form,yây1=m(xâx1)yây1=m(xâx1).Step 4.Write the equation in slope-intercept form. | https://openstax.org/books/elementary-algebra-2e/pages/4-key-concepts |
Step 1.Find the slope using the given points. | https://openstax.org/books/elementary-algebra-2e/pages/4-key-concepts |
Step 2.Choose one point. | https://openstax.org/books/elementary-algebra-2e/pages/4-key-concepts |
Step 3.Substitute the values into the point-slope form,yây1=m(xâx1)yây1=m(xâx1). | https://openstax.org/books/elementary-algebra-2e/pages/4-key-concepts |
Step 4.Write the equation in slope-intercept form. | https://openstax.org/books/elementary-algebra-2e/pages/4-key-concepts |
To Write and Equation of a LineIf given slope andy-intercept, use slopeâintercept formy=mx+by=mx+b.If given slope and a point, use pointâslope formyây1=m(xâx1)yây1=m(xâx1).If given two points, use pointâslope formyây1=m(xâx1)yây1=m(xâx1). | https://openstax.org/books/elementary-algebra-2e/pages/4-key-concepts |
If given slope andy-intercept, use slopeâintercept formy=mx+by=mx+b. | https://openstax.org/books/elementary-algebra-2e/pages/4-key-concepts |
If given slope and a point, use pointâslope formyây1=m(xâx1)yây1=m(xâx1). | https://openstax.org/books/elementary-algebra-2e/pages/4-key-concepts |
If given two points, use pointâslope formyây1=m(xâx1)yây1=m(xâx1). | https://openstax.org/books/elementary-algebra-2e/pages/4-key-concepts |
To Find an Equation of a Line Parallel to a Given LineStep 1.Find the slope of the given line.Step 2.Find the slope of the parallel line.Step 3.Identify the point.Step 4.Substitute the values into the point-slope form,yây1=m(xâx1)yây1=m(xâx1).Step 5.Write the equation in slope-intercept form. | https://openstax.org/books/elementary-algebra-2e/pages/4-key-concepts |
Step 1.Find the slope of the given line. | https://openstax.org/books/elementary-algebra-2e/pages/4-key-concepts |
Step 2.Find the slope of the parallel line. | https://openstax.org/books/elementary-algebra-2e/pages/4-key-concepts |
Step 3.Identify the point. | https://openstax.org/books/elementary-algebra-2e/pages/4-key-concepts |
Step 4.Substitute the values into the point-slope form,yây1=m(xâx1)yây1=m(xâx1). | https://openstax.org/books/elementary-algebra-2e/pages/4-key-concepts |
Step 5.Write the equation in slope-intercept form. | https://openstax.org/books/elementary-algebra-2e/pages/4-key-concepts |
To Find an Equation of a Line Perpendicular to a Given LineStep 1.Find the slope of the given line.Step 2.Find the slope of the perpendicular line.Step 3.Identify the point.Step 4.Substitute the values into the point-slope form,yây1=m(xâx1)yây1=m(xâx1).Step 5.Write the equation in slope-intercept form. | https://openstax.org/books/elementary-algebra-2e/pages/4-key-concepts |
Step 1.Find the slope of the given line. | https://openstax.org/books/elementary-algebra-2e/pages/4-key-concepts |
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