Question

3. Find the equation of a line perpendicular to y=-9x+b and through point (-18,3)​

Answer 1

y =
`(1)/(9)` x + 1

Explanation:

The equation of a line in slope- intercept form is

y = mx + b ( m is the slope and b the y- intercept )

y = - 9x + b ← is in slope- intercept 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)` , thus

y =
`(1)/(9)` x + b ← is the partial equation

To find b substitute (- 18, 3) into the partial equation

3 = 2 + b ⇒ b = 3 - 2 = 1

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