348 CHAPTER 6 Algebra, Graphs, and Functions b) The break-even point is the number of bicycles that must be sold for the company to have neither a profit nor a loss. The break-even point is where the graph intercepts the horizontal, or S-axis, for that is where the profit, P, is 0. To break even, about 1500 bicycles must be sold. The actual value can be obtained by substituting 0 for P in the equation and solving the equation for S. Do this now. c) We can estimate the answer by drawing a horizontal line from 150 on the profit axis. Since the horizontal line cuts the graph at about 4000 on the S-axis, about 4000 bicycles were sold. 7 Now try Exercise 101 Exercises Warm Up Exercises In Exercises 1–8, fill in the blank with an appropriate word, phrase, or symbols(s). 1. An illustration of all the points whose coordinates satisfy an equation is called a(n) ________. Graph 2. To determine the x-intercept of the graph of a linear equation, set ________ equal to zero and solve the equation for x. y 3. To determine the y-intercept of the graph of a linear equation, set ________ equal to zero and solve the equation for y. x 4. The ratio of the vertical change to the horizontal change for any two points on a line is called the ________ of the line. Slope 5. The three methods used to graph a linear equation given in this section are _________, _________, and ________. Plotting points, using intercepts, and using the slope and the y-intercept 6. The minimum number of points needed to graph a linear equation is ________. Two 7. In the equation y mx b, = + the slope of the line is represented by ________. m 8. a) The point whose coordinates are (2, 7) is located in the ________ quadrant. First b) The point whose coordinates are ( 3, 5) − − is located in the ________ quadrant. Third Practice the Skills In Exercises 9–16, plot the given points on the same axes. 9. (3, 1) * 10. ( 2, 4) − − * 11. ( 5, 1) − − * 12. (4, 0) * 13. (0, 2) * 14. (0, 0) * 15. (0, 5) − * 16. 2 , 5 1 2 1 2 ( ) * In Exercises 17–24, plot the given points on the same axes. 17. (4, 1) − * 18. (3, 2) * 19. ( 1, 5) − − * 20. (0, 1) − * 21. (0, 2) * 22. ( 3, 0) − * 23. (5, 1) * 24. (4.5, 3.5) * Exercises 25–34 are indicated on the graph in Fig. 6.22. Write the coordinates of the indicated point. 25. (0, 2) 26. ( 5, 4) − 27. ( 2, 0) − 28. ( 3, 1) − 29. ( 3, 4) − − 30. (0, 3) − 31. (2, 2) − 32. (4, 0) 33. (2, 2) 34. (4, 3) In Exercises 35– 42, determine which ordered pairs satisfy the given equation. 35. x y 2 3 6 + = (0, 2) (3, 0) (2, 3) (0, 2) (3, 0) 36. x y 3 5 15 − = (0, 3) − (5, 0) ( 3, 5) − (0, 3) − (5, 0) 37. ( ) − = − x y 3 2 10 (8, 7) ( 1, 4) , 0 10 3 (8, 7), ,0 10 3 ( ) 38. − = − − − x y 2 3 9 (0, 3) (2,1) ( 3, 5) (0, 3), ( 3, 5) − − − 39. = + − y x 6 3 6 (1, 1) (4, 3) (2, 5) (4, 3) 40. y x 3 4 2 (2, 1) (1, 2) 0, 2 3 ( ) = + (1, 2), 0, 2 3 ( ) 41. y x 3 8 3 = − + (8, 0) ( 8, 9) − (0, 3) (8, 0) (0, 3) 42. y x 5 7 10 = − + (14, 0) (0, 10) (7, 15) (14, 0) (0, 10) In Exercises 43–52, graph the equation by plotting points, as in Example 3. 43. y x 1 = + * 44. y x 2 = − * 45. y x2 1 = − * 46. y x2 3 = − + * SECTION 6.6 26 28 25 34 33 27 29 31 32 30 4 5 3 3 2 2 1 5 4 1 21 21 22 23 24 25 22 23 24 25 y x Figure 6.22 *See Instructor Answer Appendix
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