Answer
$y=\frac{5}{2}x-\frac{11}{2}$ for $1 \leq x \leq 5$.
Work Step by Step
$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}=\frac{7-(-3)}{5-1}=\frac{10}{4}$
$y-y_{1}=m(x-x_{1})$
$y-(-3)=\frac{10}{4}(x-1)$
$y+3=\frac{10}{4}x-\frac{10}{4}$
$y=\frac{10}{4}x-\frac{22}{4}$
$y=\frac{5}{2}x-\frac{11}{2}$
Since this is only over the range of $(1,-3)$ to $(5,7)$ this applies only to the domain of $1 \leq x \leq 5$.
