Question

the graph shows the cost for each video game rental.
what does the rate of change represent in this situation?
select from the drop - down menu to correctly complete the sentence.
the rate of change represents
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graph: x - axis: video games rented (0,1,2,3,4); y - axis: cost (dollars) (0,2,4,6,8,10,12,14,16,18,20). line passes through (0,0),(1,5),(2,10),(3,15),(4,20)

Explanation:

Step1: Identify two points on the line

We can take the points \((1, 5)\) and \((2, 10)\) from the graph (since when \(x = 1\) (video games rented), \(y = 5\) (cost in dollars), and when \(x = 2\), \(y = 10\)).

Step2: Calculate the rate of change (slope)

The formula for the rate of change (slope) between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(m=\frac{y_2 - y_1}{x_2 - x_1}\).
Substituting \(x_1 = 1\), \(y_1 = 5\), \(x_2 = 2\), \(y_2 = 10\) into the formula:
\(m=\frac{10 - 5}{2 - 1}=\frac{5}{1}=5\)

Step3: Interpret the rate of change

The \(x\)-axis represents the number of video games rented, and the \(y\)-axis represents the cost (in dollars). The rate of change (slope) is the change in \(y\) (cost) per change in \(x\) (number of video games rented). So a rate of change of 5 means that for each additional video game rented, the cost increases by 5 dollars. In other words, the rate of change represents the cost per video game rental.

Answer:

The rate of change represents the cost (in dollars) per video game rental.