In order to find the perpendicular line, we need to know that perpendicular lines have the following relation about their slopes:
[tex]m_2=-\frac{1}{m_1}[/tex]So first, let's find the slope of the given equation, putting it in the slope-intercept form (y = mx + b, m is the slope):
[tex]\begin{gathered} x-5y=-40 \\ -5y=-x-40 \\ 5y=x+40 \\ y=\frac{1}{5}x+8 \end{gathered}[/tex]The slope is m1 = 1/5. So the slope of any perpendicular line is:
[tex]m_2=-\frac{1}{\frac{1}{5}}=-5[/tex]So the perpendicular line has the model y = -5x + b
Therefore the correct option is C.
