Chapter Review 57 Section You should be able to . . . Example(s) Review Exercises 6 Find the equation of a line given two points (p. 39) 7 21–23 7 Graph lines written in general form using intercepts (p. 39) 8 7 8 Find equations of parallel lines (p. 40) 9, 10 24 9 Find equations of perpendicular lines (p. 42) 11, 12 25 1.6 1 Write the standard form of the equation of a circle (p. 48) 1 26, 27 2 Graph a circle by hand and by using a graphing utility (p. 49) 2, 3 28, 29 3 Work with the general form of the equation of a circle (p. 51) 4, 5 28, 29, 33 Review Exercises In Problems 1–4, find the following for each pair of points: (a) The distance between the points. (b) The midpoint of the line segment connecting the points. (c) The slope of the line containing the points. (d) Then interpret the slope found in part (c). 1. ( ) ( ) 0, 0 ; 4, 2 2. ( ) ( ) − − 1, 1; 2,3 5. List the intercepts of the following graph. x y 24 4 2 22 6. Graph = − + y x 15 2 using a graphing utility. Create a table of values to determine a good initial viewing window. Use a graphing utility to approximate the intercepts. 3. ( ) ( ) − 4, 4; 4,8 4. ( ) ( ) − − − 2, 1; 3, 1 In Problems 7–9, determine the intercepts and graph each equation by plotting points. Verify your results using a graphing utility. Label the intercepts on the graph. 7. − = x y 2 3 6 8. = − y x 9 2 9. + = x y2 16 2 In Problems 10–14, test each equation for symmetry with respect to the x-axis, the y-axis, and the origin. 10. = x y 2 3 2 11. + = x y4 16 2 2 12. = − − y x x3 4 4 2 13. = − y x x 3 14. + + + = x x y y2 0 2 2 15. Sketch a graph of = y x .3 In Problems 16 and 17, use a graphing utility to approximate the solutions of each equation rounded to two decimal places. All solutions lie between 10 − and 10. 16. − + = x x5 3 0 3 17. − = + x x 3 2 1 4 In Problems 18–25, find an equation of the line having the given characteristics. Express your answer using either the general form or the slope–intercept form of the equation of a line, whichever you prefer. Graph the line. 18. = − Slope 2; containing the point ( ) − 3, 1 19. = Slope 0; containing the point ( ) −5, 4 20. Slope undefined; containing the point ( ) −3, 4 21. = x-intercept 2; containing the point ( ) − 4, 5 22. = − y-intercept 2; containing the point ( ) − 5, 3 23. Containing the points ( ) − 3, 4 and ( ) 2, 1 24. Parallel to the line − = − x y 2 3 4; containing the point −( ) 5, 3 25. Perpendicular to the line − = − x y 3 4; containing the point ( ) −2, 4 In Problems 26 and 27, find the standard form of the equation of the circle whose center and radius are given. 26. ( ) ( ) = − = h k r , 2, 3 ; 4 27. ( ) ( ) = − − = h k r , 1, 2; 1
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