Answer
Choice $G$
Work Step by Step
The line in the given graph passes through $(-1,1)$ and $(0,-1)$. Using
$$
m=\frac{y_2-y_1}{x_2-x_1}
$$ or the Slope Formula where $(x_1,y_1)$ and $(x_2,y_2)$ are two points on the line, then the slope of the line in the given graph is
$$
m=\frac{1-(-1)}{-1-0}=-2
.$$
Since parallel lines have the same slope, then the needed line has to have a slope of $m=-2$ also. Furthermore, the needed line passes through $(5,-8)$. Then by the Point-Slope Form,
$$\begin{aligned}
y-y_1&=m(x-x_1)
\\
y-(-8)&=-2(x-5)
\\
y+8&=-2x+10
\\
y+2x&=2
.\end{aligned}
$$Therefore, the equation of the needed line is $y+2x=2$. Hence, Choice $G$.
