Question

Write an equation of a line in point-slope form that is perpendicular to the line y=1/2x-7 and goes through the point (4,-3)

Answer 1

y = - 2x + 5

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 - 7 ← 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, hence

y = - 2x + c ← is the partial equation of the perpendicular line

To find c substitute (4, - 3) into the partial equation

- 3 = - 8 + c ⇒ c = - 3 + 8 = 5

y = - 2x + 5 ← equation of perpendicular line