Question

Find the equation of the line passing through the point (–1, 5) and perpendicular to the line y = – 3x + 4.

Question 8 options:

A)

3y = x + 16

B)

y = –3x + 2

C)

y = –3x + 8

D)

3y = –x + 16

Answer 1

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Answer:

A) 3y = x + 16

Explanation:

The equation of a perpendicular line can be found by swapping the x- and y-coefficients and negating one of them. The constant will be chosen to match the given point.

Swapping coefficients, we get ...

-3y = x + c

Negating the y-coefficient gives ...

3y = x + c

Filling in the given point, we have ...

3(5) = -1 + c

16 = c

The equation of the perpendicular line can be written as ...

3y = x + 16 . . . . matches choice A

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Note that choice A is the only equation that gives a line with positive slope. The given equation has negative slope, so its perpendicular must have positive slope.