Question

Which of these is a point-slope equation of the line that is perpendicular to

y-3 = 4(x-10) and passes through (-3, 7)?
A. y-7 = -4(x + 3)
B. y+7= -1/4(x-3)
C. y+ 7 = 4(x - 3)
D.y-7=-1/4(x+3)​

Answer 1

D

Explanation:

The equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

y - 3 = 4(x - 10) ← is in point- slope form

with slope m = 4

Given a line with slope m then the slope of a line perpendicular to it is

`m_(perpendicular)` = -
`(1)/(m)` = -
`(1)/(4)`

The perpendicular line passes through (- 3, 7), hence

y - 7 = -
`(1)/(4)`(x - (- 3)), that is

y - 7 = -
`(1)/(4)`(x + 3) → D