Question

find the equation of a straight line passing through the point (3,3) which is perpendicular to the line y=-1/2x-4

Answer 1

y = 2x - 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 = -
`(1)/(2)` x - 4 ← is in slope- intercept form

with slope m = -
`(1)/(2)`

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

`m_(perpendicular)` = -
`(1)/(m)` = -
`(1)/(-(1)/(2) )` = 2, thus

y = 2x + c ← is the partial equation

To find c substitute (3, 3) into the partial equation

3 = 6 + c ⇒ c = 3 - 6 = - 3

y = 2x - 3 ← equation of perpendicular line