Question

Write an equation of the line passing through the point (4, –3) that is perpendicular to the line y−3=−9 (x+4).

Answer 1

see explanation

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 = - 9(x + 4) ← is in point- slope form

with slope m = - 9

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

`m_(perpendicular)` = -
`(1)/(m)` = -
`(1)/(-9)` =
`(1)/(9)`

The point (a, b) = (4, - 3), hence

y + 3 =
`(1)/(9)` (x - 4) ← equation of perpendicular line