sat suite question viewer

Algebra / Linear functions Difficulty: Medium

The graph of the function $f$ , where $y = f (x)$ , gives the total cost $y$ , in dollars, for a certain video game system and $x$ games. What is the best interpretation of the slope of the graph in this context?

Each game costs $$ 25$ .

The video game system costs $$ 100$ .

The video game system costs $$ 25$ .

Each game costs $$ 100$ .

Back question 23 of 152 Next

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152

Explanation

Choice A is correct. The given graph is a line, and the slope of a line is defined as the change in the value of $y$ for each increase in the value of $x$ by $1$ . It’s given that $y$ represents the total cost, in dollars, and that $x$ represents the number of games. Therefore, the change in the value of $y$ for each increase in the value of $x$ by $1$ represents the change in total cost, in dollars, for each increase in the number of games by $1$ . In other words, the slope represents the cost, in dollars, per game. The graph shows that when the value of $x$ increases from $0$ to $1$ , the value of $y$ increases from $100$ to $125$ . It follows that the slope is $25$ , or the cost per game is $dollar sign 25$ . Thus, the best interpretation of the slope of the graph is that each game costs $dollar sign 25$ .

Choice B is incorrect. This is an interpretation of the y-intercept of the graph rather than the slope of the graph.

Choice C is incorrect. The slope of the graph is the cost per game, not the cost of the video game system.

Choice D is incorrect. Each game costs $dollar sign 25$ , not $dollar sign 100$ .