Answer
$y=-3$
Work Step by Step
Using $y-y_1=\dfrac{y_1-y_2}{x_1-x_2}(x-x_1)$ or the two-point form of linear equations, the equation of the line passing through $\left(
\dfrac{1}{2},-3
\right)$ and $\left(
-\dfrac{2}{3},-3
\right)$ is
\begin{array}{l}\require{cancel}
y-(-3)=\dfrac{-3-(-3)}{\frac{1}{2}-\left(-\frac{2}{3}\right)}\left( x-\dfrac{1}{2} \right)
\\\\
y+3=\dfrac{0}{\frac{1}{2}+\frac{2}{3}}\left( x-\dfrac{1}{2} \right)
\\\\
y+3=0
\\\\
y=-3
.\end{array}