Question

a relation is plotted as a linear function on the coordinate plane starting at point e at(0, 27)and ending at point f at (5, -8). what is the rate of change for the linear function and what is its initial value? select from the drop-down menus to correctly complete the statements. the rate of change for the linear function is choose and the initial value is choose.

Explanation:

Step1: Calculate rate of change

The rate of change (slope) of a linear function between two points $(x_1,y_1)$ and $(x_2,y_2)$ is given by $\frac{y_2-y_1}{x_2-x_1}$. Here, $(x_1,y_1)=(0,27)$ and $(x_2,y_2)=(5,-8)$.
$\text{Rate of change} = \frac{-8 - 27}{5 - 0} = \frac{-35}{5} = -7$

Step2: Identify initial value

The initial value of a linear function is the y-value when $x=0$, which is the y-coordinate of the point where $x=0$.
Initial value = $27$

Answer:

The rate of change for the linear function is $\boldsymbol{-7}$ and the initial value is $\boldsymbol{27}$.