Answer:
3/4
Step-by-step explanation:
First of all, we need to calculate the slope of the line shown. This can be computed as:
![m=\frac{\Delta y}{\Delta x}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B%5CDelta%20y%7D%7B%5CDelta%20x%7D)
where
is the increment along the y-direction
is the increment along the x-direction
We can choose the following two points to calculate the slope of the line shown:
(-3,2) and (0,-2)
And so, the slope of the line shown is
![m=\frac{-2-(2)}{0-(-3)}=-\frac{4}{3}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B-2-%282%29%7D%7B0-%28-3%29%7D%3D-%5Cfrac%7B4%7D%7B3%7D)
Two lines are said to be perpendicular if the slope of the first line is the negative reciprocal of the slope of the second line:
![m_2 = -\frac{1}{m_1}](https://tex.z-dn.net/?f=m_2%20%3D%20-%5Cfrac%7B1%7D%7Bm_1%7D)
Using
, we find that a line perpendicular to the line shown should have a slope of
![m_2 = -\frac{1}{-4/3}=3/4](https://tex.z-dn.net/?f=m_2%20%3D%20-%5Cfrac%7B1%7D%7B-4%2F3%7D%3D3%2F4)