Which choice is the equation of a line that passes through the point (–6, –2) and is perpendicular to the line represented by this equation?
y = −3x + 1
A. 3x + y = 1
B. y = 1/3x
C. y = −3x
D. −3y = −x + 1
isn't the answer to this B, since the negative reciprocal of -3x is 1/3?
D also has slope 1/3, but the given point does indeed lie on line B.
Right
thank you both! :)
I agree,
B is the correct choice.
To determine the equation of a line that is perpendicular to another line, we need to find the negative reciprocal of the slope of the given line.
The given line has a slope of -3. The negative reciprocal of -3 is 1/3.
Now, let's check the answer choices:
A. 3x + y = 1: This equation has a slope of -3 (since it is in the form y = mx + b), so it is not perpendicular to the given line.
B. y = (1/3)x: This equation has a slope of 1/3, which is indeed the negative reciprocal of -3. Therefore, this equation represents a line that is perpendicular to the given line.
C. y = -3x: This equation has the same slope as the given line (-3), so it is not perpendicular to the given line.
D. -3y = -x + 1: To determine the slope of this line, we need to rearrange the equation into the form y = mx + b, where m represents the slope. Dividing the equation by -3, we get y = (1/3)x - 1/3. This equation has a slope of 1/3, which is the negative reciprocal of -3. Therefore, this equation represents a line that is perpendicular to the given line.
So, both answer choices B and D have equations that are perpendicular to the given line.