a. Plot each pair of points, where x is the number of years after 1980 and y is the number of domestic movies released. b. Interpret the meaning of the first and last ordered pairs in the table. c. What can you conclude, if anything, about the number of domestic movies released? 106. The table shows the average price of a U.S. movie ticket in a given year. (Source: www.boxofficemojo.com) Year 2001 2002 2003 2004 2005 2006 2007 2008 Average price 5.66 5.81 6.03 6.21 6.40 6.58 6.88 7.08 (in dollars) a. Plot each pair of points, where x is the year and y is the average price of a U.S. movie ticket. b. Interpret the meaning of the first and last ordered pairs in the table. c. What can you conclude, if anything, about the average price of a U.S. movie ticket? You Be the Teacher! Answer each student’s questions. 107. Gunnar: Is there an easy way to graph ordered pairs with large numbers like (-16, 23) without drawing too many tick marks? 108. Sherry: Is there an easy way to determine if a point is a solution of an equation other than looking at the graph? Correct each student’s errors, if any. 109. Determine if the point (-25, -33) is a solution of y = |x + 14| -12. Lisa’s work: y = |x + 14| -12 -33 = |-25 + 14| -12 -33 = |-11| - 12 -33 = -11 - 12 -33 = -33 True Since the statement is true, (-25, -33) is a solution of the equation. 110. Determine if the point a3 2 , 12b is a solution of the equation y = -8x2 + 4x. Harrison’s work: y = -8x2 + 4x. 12 = -8 a3 2 b 2 + 4a3 2 b 12=-8a9 4 b + 2 · 3 12 = -2 · 9 + 6 12 = -18 + 6 12 = -12 True Since the statement is true, a3 2 , 12b is a solution of the equation. Calculate It! Use the TABLE feature of a graphing calculator to find five solutions of each equation. 111. y = 43x2 - 12x + 5 112. y = -5x3 + 9x2 + 13 113. y = 3x - 7 2 114. y = 6 - 4x 5 Think About It! 115. The ordered pair (3, -1) is a solution of y = 2 3 x + b. What value of b makes this possible? 116. The ordered pair a1 2 , 5b is a solution of y = -4x + b. What value of b makes this possible? 117. The ordered pair (a, -2) is a solution of y = |x + 1| -3. What value(s) of a makes this possible? 118. The ordered pair (a, 6) is a solution of y = |2x + 3| -5. What value(s) of a makes this possible. 119. Suppose the midpoint between two points (x, -6) and (4, y) is (-3, 1). Find the values of x and y. 120. Suppose the midpoint between two points (x, 9) and (-2, y) is (-5, 6). Find the values of x and y. 164 Chapter 3 Graphs, Relations, and Functions
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