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](https://tex.z-dn.net/?f=y%20%3D%20mx%2Bb)
where
is the slope
is the y-intercept
Step 1:
Finding the slope of the given equation
The given equation is
![y = 2x - 6](https://tex.z-dn.net/?f=y%20%3D%202x%20-%206)
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}](https://tex.z-dn.net/?f=-%5Cfrac%7B1%7D%7Bm%7D%3D-%5Cfrac%7B1%7D%7B2%7D)
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.
<u>Verification:</u>
The slope of the given line:
![m_1=2](https://tex.z-dn.net/?f=m_1%3D2)
The slope of the perpendicular line:
![m_2=-\frac{1}{2}\:\:\:\:](https://tex.z-dn.net/?f=m_2%3D-%5Cfrac%7B1%7D%7B2%7D%5C%3A%5C%3A%5C%3A%5C%3A)
The product of the slopes is:
![\:m_1\times \:m_2\:=2\times -\frac{1}{2}\:\:=-1](https://tex.z-dn.net/?f=%5C%3Am_1%5Ctimes%20%5C%3Am_2%5C%3A%3D2%5Ctimes%20-%5Cfrac%7B1%7D%7B2%7D%5C%3A%5C%3A%3D-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.