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:
[tex]m=\frac{\Delta y}{\Delta x}[/tex]
where
[tex]\Delta y = y_2-y_1[/tex] is the increment along the y-direction
[tex]\Delta x = x_2 - x_1[/tex] 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
[tex]m=\frac{-2-(2)}{0-(-3)}=-\frac{4}{3}[/tex]
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:
[tex]m_2 = -\frac{1}{m_1}[/tex]
Using [tex]m_1 = -\frac{4}{3}[/tex], we find that a line perpendicular to the line shown should have a slope of
[tex]m_2 = -\frac{1}{-4/3}=3/4[/tex]
