Answer
The function is f($x$) = $\frac{5}{2}$$x$ - $\frac{11}{2}$
Work Step by Step
The equation of a line connecting two points is
$y$ - $y_{1}$ = $m$($x$ - $x_{1}$) and $m$ = $\frac{y_{2} - y_{1}}{x_{2} - x_{1}}$. Substituting we get
$m$ = $\frac{7 - (-3)}{5 - 1}$ = $\frac{5}{2}$ and $y$ - (-3) = $\frac{5}{2}$($x$ - 1) which is f($x$) = $\frac{5}{2}$$x$ - $\frac{11}{2}$
for 1$\leq$$x$$\leq$5
