Write the equation of the line that passes through the point P(6, -4) and is perpendicular to the line y = (1/2)x + 7.

Question

a. y = (1/2)x - 4

b. y = (1/2)x + 7

c. y = -2 + 8

y = -2 + 7

Answer 1

When something is perpendicular, we take the negative reciprocal of the base line's slope. In this case, it's ¹/₂. So we flip the numerator with the denominator, and multiply by -1, and that gives us -2. That alone knocks out choices a and b.

 

From here, we're given a point, so what we need to use is the point-slope formula:

y - y₁ = m(x - x₁)

Point P = (6, -4)

y - (-4) = -2(x - 6)

y + 4 = -2x + 12

Subtract 4:

y = -2x + 8