Question

find the rate of change and initial value for the linear function.
the rate of change is
(simplify your answer.)

Explanation:

Step1: Pick two points on the line

Choose points $(0, 5)$ and $(10, 0)$ from the graph.

Step2: Calculate rate of change

Use slope formula $\frac{y_2-y_1}{x_2-x_1}$.
$\frac{0 - 5}{10 - 0} = \frac{-5}{10} = -\frac{1}{2}$

Step3: Identify initial value

The initial value is the y-intercept, where $x=0$. From the point $(0,5)$, the initial value is 5.

Answer:

The rate of change is $\boldsymbol{-\frac{1}{2}}$ and the initial value is $\boldsymbol{5}$.