Write the equation of the line that has a slope of -2 and y-intercept of 1.
1 answer:
Answer:
The equation of the line that has a slope of -2 and y-intercept of 1 will be:
- y = -2x+1
Step-by-step explanation:
The slope-intercept form of the line equation
where
- m is the slope
- b is the y-intercept
Given
The slope m = -2
y-intercept b = 1
We know that the value of y-intercept can be determined by setting x = 0, and determining the corresponding value of y.
It is already stated that the y-intercept = -1
It means at y = 1, x = 0
Thus, we have the point (0, 1)
Now using the slope-intercept form
y = mx+b
substituting m = -2 and b = 1
y = -2x + (1)
y = -2x+1
Therefore, the equation of the line that has a slope of -2 and y-intercept of 1 will be:
- y = -2x+1
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In order to check if the lines are perpendicular, we need to check if their slopes have the following relation (to find the slope we can use the slope-intercept form y = mx + b):
A.
In this option, y = -5 is an horizontal line and x = 2 is a vertical line, therefore they are perpendicular.
B.
First let's find the slope of each line:
These slopes obey the relation stated above, so the lines are perpendicular.
C.
These slopes obey the relation stated above, so the lines are perpendicular.
D.
These slopes obey the relation stated above, so the lines are perpendicular.
E.
These slopes don't obey the relation stated above, so the lines aren't perpendicular.
The correct options are A, B, C and D.