Answer
$f(x)=\dfrac{1}{2}x+\dfrac{7}{2}$
Work Step by Step
Using $y-y_1=m(x-x_1)$ or the Point-Slope Form of Linear Equations, then the equation of the line with slope $\dfrac{1}{2}$ and containing the point $(-1,3)$ is
\begin{array}{l}\require{cancel}
y-3=\dfrac{1}{2}(x-(-1))
\\\\
y-3=\dfrac{1}{2}(x+1)
\\\\
y-3=\dfrac{1}{2}x+\dfrac{1}{2}
\\\\
y=\dfrac{1}{2}x+\dfrac{1}{2}+3
\\\\
y=\dfrac{1}{2}x+\dfrac{1}{2}+\dfrac{6}{2}
\\\\
y=\dfrac{1}{2}x+\dfrac{7}{2}
.\end{array}
In function notation, this is equivalent to $
f(x)=\dfrac{1}{2}x+\dfrac{7}{2}
.$
