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: 2, 5, 8; distance from home (mi), y: 12, 18, 24. what is the rate of change?

Explanation:

Step1: Recall rate - of - change formula

The rate of change (slope) formula for a linear function is $m=\frac{y_2 - y_1}{x_2 - x_1}$, where $(x_1,y_1)$ and $(x_2,y_2)$ are two points on the line.

Step2: Select two points

Let's take the points $(2,12)$ and $(5,18)$ from the table. Here $x_1 = 2,y_1=12,x_2 = 5,y_2 = 18$.

Step3: Calculate the rate of change

$m=\frac{18 - 12}{5 - 2}=\frac{6}{3}=2$.

Answer:

2