Question

jasmine is hiking at a state park. her distance from home, y, is a function of the time she hikes, x. the table and graph both represent the function. time (h), x distance from home (mi), y 2 12 5 18 8 24 what is the rate of change?

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: Select two points from table

Use \((2, 12)\) and \((5, 18)\).

Step3: Calculate rate of change

Substitute into formula: \(\frac{18 - 12}{5 - 2}=\frac{6}{3} = 2\). Check with another pair, e.g., \((5, 18)\) and \((8, 24)\): \(\frac{24 - 18}{8 - 5}=\frac{6}{3}=2\).

Answer:

2