Question

1. what is the rate of change of y with respect to x of the function shown below?

Explanation:

Step1: Select two points

Let's take two points on the line, say $(x_1,y_1)=(0, - 2)$ and $(x_2,y_2)=(4,0)$.

Step2: Use slope - formula

The rate of change (slope $m$) of a linear function $y$ with respect to $x$ is given by the formula $m=\frac{y_2 - y_1}{x_2 - x_1}$.
Substitute the values: $m=\frac{0-(-2)}{4 - 0}=\frac{2}{4}=\frac{1}{2}$.

Answer:

$\frac{1}{2}$