Answer
$g(x)=-\frac{1}{4}x+9$
Work Step by Step
$g(0)=9$ can be written as $(0,9)$ and $g(8)=7$ as $(8,7)$.
Slope $m$ of the line that passes through $(0,9)$ and $(8,7)$ is
$m=\frac{7-9}{8-0}=-\frac{2}{8}=-\frac{1}{4}$
Because the line crosses the y-axis at $(0,9)$, the y-intercept $b$ is $9$.
$y=mx+b$
Substituting the values of $m$ and $b$, we get
$y=-\frac{1}{4}x+9$
A function is $g(x)=-\frac{1}{4}x+9$
