Answer
$y=-6$
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 $(-3,4)$ and $(-5,-2)$ is
$m_{1}=\displaystyle \frac{-2-4}{-5-(-3)}=\frac{-6}{-2}=3$
The line passing through $(1,y)$ and $(7,12)$ has the slope
$m_{2}=\displaystyle \frac{12-y}{7-1}=\frac{12-y}{6}$
Since the lines a re parallel, $m_{1}=m_{2}$
$\displaystyle \frac{12-y}{6}=3\qquad $... multiply with $6$,
$12-y=18 \qquad $... add $y-18$
$12-18=y$
$y=-6$
