The line given passes through two points. These are (-6,0) and (0,-8).
Remember that two lines are perpendicular if the product of their slopes is -1. So, the first thing we're going to do is to find the slope of the line given.
The slope between two points (x1,y1) and (x2,y2) can be found using the formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
If we replace our values:
[tex]m=\frac{-8-0}{0-(-6)}=\frac{-8}{6}=-\frac{4}{3}[/tex]
To find other perpendicular line to this one, we have to find a number which multiplication with -4/3 is -1.
This number is clearly 3/4. Because
[tex]\begin{gathered} m_1\cdot m_2=-1 \\ -\frac{4}{3}\cdot m_2=-1 \\ \\ m_2=\frac{3}{4} \\ \\ -\frac{4}{3}\cdot\frac{3}{4}=-1 \end{gathered}[/tex]
Therefore, the slope of the perpendicular line must be 3/4, and the original slope is -4/3.
If we graph this:
