The graph of the function f , where y = f ( x ) , gives the total cost y

Question

The graph of the function f , where y &#x0003D; f &#x00028; x &#x00029; , 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?

Accepted Answer

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&rsquo;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 $ 25 . Thus, the best interpretation of the slope of the graph is that each game costs $ 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 $ 25 , not $ 100 .

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