Question

Find the equation of the line perpendicular to y=2x-6 that passes through the point (1,5). If possible, write the equation in slope-intercept form.

Answer 1

y = -
`(1)/(2)` x +
`(11)/(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 = 2x - 6 ← is in slope- intercept form

with slope m = 2

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

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

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

To find c substitute (1, 5) into the partial equation

5 = -
`(1)/(2)` + c ⇒ c = 5 +
`(1)/(2)` =
`(11)/(2)`

y = -
`(1)/(2)` x +
`(11)/(2)` ← equation of perpendicular line