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
where
is the slope
is the y-intercept
Step 1:
Finding the slope of the given equation
The given equation is
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:
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:
The slope of the perpendicular line:
The product of the slopes is:
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.