Answer
a) $f(x)=\dfrac{2}{3}x-2$
b) See graph
Work Step by Step
We are given the linear function:
$f\left(\dfrac{1}{2}\right)=-\dfrac{5}{3}$
$f(6)=2$
a) Determine the slope of the line using the points $\left(\dfrac{1}{2},-\dfrac{5}{3}\right),(6,2)$:
$m=\dfrac{2-\left(-\dfrac{5}{3}\right)}{6-\dfrac{1}{2}}=\dfrac{\dfrac{11}{3}}{\dfrac{11}{2}}=\dfrac{2}{3}$
Determine the line's equation using the slope and one of the points:
$y-2=\dfrac{2}{3}(x-6)$
$y=\dfrac{2}{3}x-4+2$
$f(x)=\dfrac{2}{3}x-2$
b) Graph the function using the two points:
