Answer
$y=2$
Work Step by Step
Use: $m=\displaystyle \frac{\text{change in y}}{\text{change in x}}=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$,
Parallel lines have equal slopes.
The slope of the line passing through $(2,3)$ and $(-2,1)$ is
$m_{1}=\displaystyle \frac{1-3}{-2-2}=\frac{-2}{-4}=\frac{1}{2}$
The line passing through $(5,y)$ and $(1,0)$ has the slope
$m_{2}=\displaystyle \frac{0-y}{1-5}=\frac{-y}{-4}=\frac{y}{4}$
Since the lines a re parallel, $m_{1}=m_{2}$
$\displaystyle \frac{y}{4}=\frac{1}{2}\qquad $ ... multiply with 4,
$y=2$
