Answer
$ g(x)=\frac{1}{2}x+2$
Work Step by Step
$g(2)=3$ can be written as $(2,3)$ and $g(6)=5$ as $(6,5)$
Slope $m=\frac{5-3}{6-2}=\frac{2}{4}=\frac{1}{2}$
Point-slope form is
$y-y_{1}=m(x-x_{1})$
Using the values of slope $m$ and point $(6,5)$, we get
$y-5=\frac{1}{2}(x-6)$
$\implies y-5=\frac{1}{2}x-3$
$\implies y=\frac{1}{2}x-3+5$
$\implies y=\frac{1}{2}x+2$
A function is
$ g(x)=\frac{1}{2}x+2$
