Question

find the equation of the line passing through the point (0,1) which is perpendicular to the line y=-3/4x-3

Answer 1

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

Explanation:

The equation of a line in slope- intercept form is

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

y = -
`(3)/(4)` x - 3 ← is in slope- intercept form

with slope m = -
`(3)/(4)`

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

`m_(perpendicular)` = -
`(1)/(m)` = -
`(1)/(-(3)/(4) )` =
`(4)/(3)`

The line crosses the y- axis at (0, 1 ) ⇒ c = 1

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