Answer
$f(x)=2x-7$
Work Step by Step
We can rewrite $f(3)=-1$ as $(3,-1)$ and $f(-4)=-15$ as $(-4,-15)$.
The slope of the line that passes through $(3,-1)$ and $(-4,-15)$ is
$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}=\frac{-15-(-1)}{-4-3}=2$
Equation of the line is
$y-y_{1}=m(x-x_{1})$
$\implies y-(-1)=2(x-3)$
$\implies y+1=2x-6$ or $y=2x-7$
A function is $f(x)=2x-7$.
