32 CHAPTER 1 Graphs Concepts and Vocabulary 3. To solve an equation of the form { } = x expression in 0 using a graphing utility, we graph { } = Y x expression in 1 and use to determine each x -intercept of the graph. 4. True or False In using a graphing utility to solve an equation, exact solutions are always obtained. Skill Building In Problems 5–16, use a graphing utility to approximate the real solutions, if any, of each equation rounded to two decimal places. All solutions lie between −10 and 10. 5. − + = x x4 2 0 3 6. − + = x x8 1 0 3 7. − + = − x x 2 5 3 2 4 8. − + = − x x 1 2 3 4 2 9. − + − = x x x 2 3 1 0 4 3 10. − + − = x x x 3 4 5 0 4 3 2 11. − − + + = x x x 5 3 7 2 2 0 3 2 12. − + + − + = x x x x 3 7 3 15 2 2 0 4 3 2 13. − − + = − + x x x x 2 3 2 5 2 2 3 1 2 4 3 2 14. − = − x x x 1 4 5 1 5 4 3 2 15. − + + = x x x 5 2 11 0 4 2 16. − + − − = x x x 3 8 2 9 0 4 2 17. ( ) ( ) + = − x x 2 3 2 3 4 18. ( ) − = − x x 3 2 2 1 19. ( ) − + = − x x x 8 2 1 3 13 In Problems 17–36, solve each equation algebraically. Verify your solution using a graphing utility. 20. ( ) − − = − x x 5 2 1 10 21. + + + = x x 1 3 2 7 5 22. + + = x x 2 1 3 16 3 23. + = y y 5 4 3 24. − = y y 4 5 18 2 25. ( )( ) ( ) + − = + x x x 7 1 1 2 26. ( )( ) ( ) + − = − x x x 2 3 3 2 27. − − = x x3 28 0 2 28. − − = x x7 18 0 2 31. + − − = x x x4 4 0 3 2 32. + − − = x x x 2 9 18 0 3 2 30. = + x x 5 13 6 2 29. = + x x 3 4 4 2 35. + + − = − x x 2 2 3 1 8 5 36. + − − = x x 1 1 5 4 21 4 34. − = x 2 3 33. + = x 1 4 ‘Are You Prepared?’ Answers 1. { } − − 2, 1 2 2. { }3 Figure 47 Rise Line Run 1.5 Lines OBJECTIVES 1 Calculate and Interpret the Slope of a Line (p. 32) 2 Graph Lines Given a Point and the Slope (p. 35) 3 Find the Equation of a Vertical Line (p. 36) 4 Use the Point–Slope Form of a Line; Identify Horizontal Lines (p. 36) 5 Use the Slope–Intercept Form of a Line (p. 37) 6 Find the Equation of a Line Given Two Points (p. 39) 7 Graph Lines Written in General Form Using Intercepts (p. 39) 8 Find Equations of Parallel Lines (p. 40) 9 Find Equations of Perpendicular Lines (p. 42) In this section we study a certain type of equation that contains two variables, called a linear equation, and its graph, a line . 1 Calculate and Interpret the Slope of a Line Consider the staircase illustrated in Figure 47. Each step contains exactly the same horizontal run and the same vertical rise . The ratio of the rise to the run, called the slope , is a numerical measure of the steepness of the staircase. For example, if the run
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