First, we have to find the slope of the given line.
We use the following formula to find the slope.
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Let's replace the points (-3, -4) and (5, 0) in the formula.
[tex]m=\frac{0-(-4)}{5-(-3)}=\frac{4}{5+3}=\frac{4}{8}=\frac{1}{2}[/tex]
The slope of the given line is 1/2.
Now, we find the slope of the new perpendicular line with the following formula.
[tex]\begin{gathered} m\cdot m_1=-1 \\ m\cdot\frac{1}{2}=-1 \\ m=-2 \end{gathered}[/tex]
The slope of the given perpendicular line is -2.
Notice that C is the only equation that has a slope of -2 because the coefficient of x is -2.
Therefore, the answer is C.
