Question

What is the slope of a line that is perpendicular to the line shown.

Answer 1

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:

$m=\frac{\Delta y}{\Delta x}$

where

$\Delta y = y_2-y_1$ is the increment along the y-direction

$\Delta x = x_2 - x_1$ 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

$m=\frac{-2-(2)}{0-(-3)}=-\frac{4}{3}$

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:

$m_2 = -\frac{1}{m_1}$

Using $m_1 = -\frac{4}{3}$, we find that a line perpendicular to the line shown should have a slope of

$m_2 = -\frac{1}{-4/3}=3/4$