Answer
a) $f(x)=\dfrac{5}{2}x-\dfrac{1}{2}$
b) See graph
Work Step by Step
We are given the linear function:
$f(-3)=-8$
$f(1)=2$
a) Determine the slope of the line using the points $(-3,-8),(1,2)$:
$m=\dfrac{2-(-8)}{1-(-3)}=\dfrac{5}{2}$
Determine the line's equation using the slope and one of the points:
$y-2=\dfrac{5}{2}(x-1)$
$y=\dfrac{5}{2}x-\dfrac{5}{2}+2$
$f(x)=\dfrac{5}{2}x-\dfrac{1}{2}$
b) Graph the function using the two points:
