Answer
a) $f(x)=\dfrac{5}{2}x-1$
b) see graph
Work Step by Step
We are given the linear function:
$f\left(\dfrac{3}{5}\right)=\dfrac{1}{2}$
$f(4)=9$
a) Determine the slope of the line using the points $\left(\dfrac{3}{5},\dfrac{1}{2}\right),(4,9)$:
$m=\dfrac{9-\dfrac{1}{2}}{4-\dfrac{3}{5}}=\dfrac{\dfrac{17}{2}}{\dfrac{17}{5}}=\dfrac{5}{2}$
Determine the line's equation using the slope and one of the points:
$y-9=\dfrac{5}{2}(x-4)$
$y=\dfrac{5}{2}x-10+9$
$f(x)=\dfrac{5}{2}x-1$
b) Graph the function using the two points:
