Question

Find the equation of the straight line passing through the point (4,8) and which is

perpendicular to the line with equation y = -3x + 2.​

Answer 1

y =
`(1)/(3)` x +
`(20)/(3)`

Explanation:

The equation of a line in slope- intercept form is

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

y = - 3x + 2 ← is in slope- intercept form

with slope m = - 3

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

`m_(perpendicular)` = -
`(1)/(m)` = -
`(1)/(-3)` =
`(1)/(3)`, thus

y =
`(1)/(3)` x + c ← is the partial equation

To find c substitute (4, 8) into the partial equation

8 =
`(4)/(3)` + c ⇒ c = 8 -
`(4)/(3)` =
`(20)/(3)`

y =
`(1)/(3)` x +
`(20)/(3)` ← equation of line