Question

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

Answer options: 2/3, -3, 3, -1/3

Answer 1

Slope of perpendicular line is 3

Explanation:

We have given a figure in which a line is given.

We have to find the slope of the line that is perpendicular to give line.

Let (x₁,y₂) = (0,3) and (x₂,y₂) = (3,2)

The formula to find the slope of the line

Slope = m = y₂-y₁/x₂-x₁

Putting given values in above formula, we have

Slope = m = 2-3 / 3-0

Slope = m = -1/3

Perpendicular lines have slopes negative reciprocal to each other.

Hence, slope of perpendicular line is
`-((1)/(-1/3))`

Hence, slope of perpendicular line is 3.

Answer 2

3

Explanation:

First of all, we need to calculate the slope of the line shown. This can be computed as:

`m=(\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:

(0,3) and (3,2)

Therefore, the slope of the line shown is

`m=(2-3)/(3-0)=-(1)/(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 = -(1)/(m_1)`

Using
`m_1 = -(1)/(3)`, we find that a line perpendicular to the line shown should have a slope of

`m_2 = -(1)/(-1/3)=3`