Answer: y = 4
Explanation:
Since line a and line b are parallel, they will have the same slope.
slope (m) for line a is:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{5-1}{4-(-2)}=\dfrac{4}{6}\quad \rightarrow \quad m=\large\boxed{\dfrac{2}{3}}[/tex]
Next, use the Point-Slope formula on line b to find y:
[tex]y_2-y_1=m(x_2-x_1)\\\\(x_1, y_1)=(-4,-4)\qquad (x_2,y_2)=(8.y)\qquad m=\dfrac{2}{3}\\\\\\y-(-4)=\dfrac{2}{3}\bigg(8-(-4)\bigg)\\\\\\y+4=\dfrac{2}{3}(12)\\\\\\y+4=2(4)\\\\\\y+4=8\\\\\\\large\boxed{y=4}[/tex]
