Question

What is the slope of a line that is perpendicular to the line y = 2x – 6?

Answer 1

Answer:

The slope of a line that is perpendicular to the line y = 2x – 6 is -1/2.

Step-by-step explanation:

The slope-intercept form of the line equation

$y = mx+b$

where

• $m$ is the slope

• $b$ is the y-intercept

Step 1:

Finding the slope of the given equation

The given equation is

$y = 2x - 6$

comparing with the slope-intercept form of the line equation

The slope of the equation is: m = 2

Step 2:

Determining the slope of the perpendicular line

In Mathematics, a line perpendicular to another line has a slope that is the negative reciprocal of the slope of the other line.

• As the slope of the equation is: m = 2

Therefore, the slope of the new perpendicular line:

$-\frac{1}{m}=-\frac{1}{2}$

Hence, the slope of a line that is perpendicular to the line y = 2x – 6 is -1/2.

Important Tip:

• The product of the slopes of perpendicular lines is -1.

Verification:

The slope of the given line:

$m_1=2$

The slope of the perpendicular line:

$m_2=-\frac{1}{2}\:\:\:\:$

The product of the slopes is:

$\:m_1\times \:m_2\:=2\times -\frac{1}{2}\:\:=-1$

As the product of the slopes of perpendicular lines is -1, therefore, the lines are perpendicular.

Thus, the slope of a line that is perpendicular to the line y = 2x – 6 is -1/2.