Question

Write the equation of the line that is perpendicular to the line y=2x+1 and passes through the point 4,6

Answer 1

y = -
`(1)/(2)` x + 8

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 + 1 ← 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)` , then

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

To find c substitute (4, 6 ) into the partial equation

6 = - 2 + c ⇒ c = 6 + 2 = 8

y = -
`(1)/(2)` x + 8 ← equation of perpendicular line