Question

The equation of line GH is y=4x-3. Write an equation of Aline perpendicular to line GH in slope-intercept form that contains point (2,3)

Answer 1

y = -
`(1)/(4)` x +
`(7)/(2)`

Explanation:

The equation of a line in slope- intercept form is

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

y = 4x - 3 is in this form with slope m = 4

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

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

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

To find c substitute (2, 3) into the partial equation

3 = -
`(1)/(2)` + c ⇒ c = 3 +
`(1)/(2)` =
`(7)/(2)`

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