Question

find the rate of change and initial value for the linear function.
a) the rate of change (slope) is

b) the initial value (y - intercept) is

Explanation:

Step1: Identify two points on line

Choose points $(x_1,y_1)=(7,0)$ and $(x_2,y_2)=(0,-7)$

Step2: Calculate slope (rate of change)

Use slope formula: $m=\frac{y_2-y_1}{x_2-x_1}$
$\frac{-7-0}{0-7}=\frac{-7}{-7}=1$

Step3: Identify y-intercept (initial value)

The y-intercept is the y-value where $x=0$, which is $-7$.

Answer:

a) The rate of change (slope) is $1$
b) The initial value (y-intercept) is $-7$