Answer
$f(x)=-\frac{5}{3}x+18$
Work Step by Step
Rewrite as shown below.
$f(6)=8$ as $(6,8)$
and $f(9)=3$ as $(9,3)$
Let $(x_1,y_1)=(6,8)$ and $(x_2,y_2)=(9,3)$.
Slope
$\Rightarrow m =\frac{y_2-y_1}{x_2-x_1}$
Substitute all the values.
$\Rightarrow m =\frac{3-8}{9-6}$
Simplify.
$\Rightarrow m =-\frac{5}{3}$
The point-slope form.
$\Rightarrow y-y_1=m(x-x_1)$
Substitute all the values.
$\Rightarrow y-8=-\frac{5}{3}(x-6)$
Simplify.
$\Rightarrow y-8=-\frac{5}{3}x+10$
Add $8$ to each side.
$\Rightarrow y-8+8=-\frac{5}{3}x+10+8$
Simplify.
$\Rightarrow y=-\frac{5}{3}x+18$
Hence, the function is $f(x)=-\frac{5}{3}x+18$.
