Chapter 11 GRAPHS OF LINEAR EQUATIONS

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1 Chapter 11 GRAPHS OF LINEAR EQUATIONS 11.1 Graphs and Applications of Linear Equations Learning Objectives A Plot points associated with ordered pairs of numbers; determine the quadrant in which a point lies. B Find the coordinates of a point on a graph. C Determine whether an ordered pair is a solution of an equation with two variables. D Graph linear equations of the type y = mx + b and Ax + By = C, identifying the y- intercept. E Solve applied problems involving graphs of linear equations. Key Terms Use the vocabulary terms listed below to complete each statement in Exercises 1 6. axes coordinates graph ordered pair origin y-intercept 1. We graph number pairs on a plane using two perpendicular number lines called. 2. On the plane, the perpendicular number lines cross at a point called the. 3. The numbers in an ordered pair are called. 4. The notation (3, 2) is an example of a(n). 5. The of an equation is a drawing that represents all its solutions. 6. A graph crosses the y-axis at the. Copyright 2012 Pearson Education, Inc. Publishing as Addison-Wesley 241

2 GUIDED EXAMPLES AND PRACTICE Objective A Plot points associated with ordered pairs of numbers; determine the quadrant in which a point lies. Review these examples for Objective A: 1. Plot the point (3, 2). The first coordinate is positive, so starting at the origin, move 3 units to the right. The second coordinate is negative, so we then move down 2 units. Practice these exercises: 1. Which point is ( 2, 4)? 2. In which quadrant is the point ( 3, 5) located? Both coordinates are negative, so ( 3, 5) is in quadrant III. 2. In which quadrant is the point (2, 1) located? Objective B Find the coordinates of a point on a graph. Review this example for Objective B: 3. Find the coordinates of point P. 3. Find the coordinates of point M. Point P is 3 units to the left of the origin and 0 units up or down. Its coordinates are ( 3, 0). 242 Copyright 2012 Pearson Education, Inc. Publishing as Addison-Wesley

3 Objective C Determine whether an ordered pair is a solution of an equation with two variables. Review this example for Objective C: 4. Determine whether ( 2, 2) is a solution of 2b a 6. 2b a TRUE 4. Determine whether ( 4, 1) is a solution of n m 5. Objective D Graph linear equations of the type y = mx + b and Ax + By = C, identifying the y-intercept. Review this example for Objective D: 5. Graph y 3 x 2 and identify the y-intercept. 2 From the equation, we see that the y-intercept is (0, 2). We find two other pairs that are solutions, using multiples of 2 to avoid fractions. Then we complete and label the graph. x y Graph x 4y 4 and identify the y-intercept. Objective E Solve applied problems involving graphs of linear equations. Review this example for Objective E: 6. The weekly salary of a salesperson at Shoe City is given by the equation w s, where s is that person s sales for the week. Graph the equation and then use the graph to estimate the salesperson s sales when the week s pay is $375. We choose some values for s and find the corresponding w-values. When s = 1000, w When s = 3000, w The cost c, in dollars of renting a 20-ft moving van at Rent King is given by the equation c 0.45m 59.95, where m is the number of miles the truck is driven. Graph the equation and then use the graph to estimate how far a van can be driven on a budget of $150. Copyright 2012 Pearson Education, Inc. Publishing as Addison-Wesley 243

4 When s = 5000, w Plot these points and draw the graph. To estimate the sales when the week s pay is $375, locate 375 on the w-axis, go across horizontally to the graph, and then go down vertically to the s-axis. We find that sales are about $4400 when a week s pay is $375. ADDITIONAL EXERCISES Objective A Plot points associated with ordered pairs of numbers; determine the quadrant in which a point lies. For extra help, see Examples 1 2 on page 785 of your text and the Section 11.1 lecture video. 1. Plot and label the set of points. 3, 2, 1, 4, 2, 2, 0, 3, 3, 4, 0, 5, 4, 0, 1, 0 In which quadrant is each point located? 2. 8, , Copyright 2012 Pearson Education, Inc. Publishing as Addison-Wesley

5 Complete each sentence using the words positive or negative or the numerals I, II, III, or IV. 4. In quadrants III and, the first coordinate is always. 5. In quadrants IV and, the second coordinate is always. Objective B Find the coordinates of a point on a graph. For extra help, see Example 3 on page 786 of your text and the Section 11.1 lecture video. Determine the coordinates of the points from the given graph. 6. A and B 7. C and D 8. E and F Objective C Determine whether an ordered pair is a solution of an equation with two variables. For extra help, see Examples 4 5 on pages of your text and the Section 11.1 lecture video. Determine whether each ordered pair is a solution of the given equation. 9. 2, 1 ; x 4 y , 7 ; y 2x , 5 ; p q , 2 ; 2d c 8 Copyright 2012 Pearson Education, Inc. Publishing as Addison-Wesley 245

6 Objective D Graph linear equations of the type y = mx + b and Ax + By = C, identifying the y-intercept. For extra help, see Examples 6 10 on pages of your text and the Section 11.1 lecture video. Graph the equation and identify the y-intercept. 13. y 2 x 14. y x x y x 2y Copyright 2012 Pearson Education, Inc. Publishing as Addison-Wesley

7 Objective E Solve applied problems involving graphs of linear equations. For extra help, see Example 11 on pages of your text and the Section 11.1 lecture video. The average annual expenditure on home insurance can be approximated by H = 21n + 414, where n is the number of years since Find the average annual home insurance cost in 1996 (n = 1), 1998, 2004, and Graph the equation and use the graph to estimate what the average annual home insurance expenditure was in n H The value V, in dollars, of a digital camera is given by V = 75t+ 450, where t is the number of years since the camera was purchased. 19. Find the value of the camera after 0 yr, 3 yr, and 6 yr. 20. Graph the equation and then use the graph to estimate the value of the camera after 4 yr. t V Copyright 2012 Pearson Education, Inc. Publishing as Addison-Wesley 247