Question

finding rate of change from a graph
an indoor trampoline park has an admission fee, plus an hourly charge. the graph displays the total cost from 3, 4, 5, and 6 hours of play. determine the hourly charge, assuming the relationship is linear
rate of change = $\square$ per hour
(graph with points (3, 18.5), (4, 23), (5, 27.5), (6, 32))

Explanation:

Step1: Recall rate of change formula

The rate of change (slope) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is \(\frac{y_2 - y_1}{x_2 - x_1}\).

Step2: Choose two points

Let's take \((3, 18.5)\) and \((4, 23)\). Here, \(x_1 = 3\), \(y_1 = 18.5\), \(x_2 = 4\), \(y_2 = 23\).

Step3: Calculate rate of change

Substitute into the formula: \(\frac{23 - 18.5}{4 - 3}=\frac{4.5}{1} = 4.5\). We can verify with other points, e.g., \((4,23)\) and \((5,27.5)\): \(\frac{27.5 - 23}{5 - 4}=\frac{4.5}{1}=4.5\), or \((5,27.5)\) and \((6,32)\): \(\frac{32 - 27.5}{6 - 5}=\frac{4.5}{1}=4.5\).

Answer:

\(4.5\)