Question

Write the equation of a line perpendicular to y=-2x+1 that passes through the point (2,3)

Answer 1

y = 1/2x + 2

Explanation:

First you have to determine the slope which is the opposite reciprocal of the slope of the line given.

So we take the slope -2 and reciprocate and by flipping the numerator and denominator which makes it -1/2.

Then we have to make it the opposite, like making a negative into a positive or a positive into a negative. So that would make it positive 1/2.

We now have the slope which is 1/2 and not we have to make sure it goes through point (2,3).

To do that, we must adjust the y-intercept until it goes through that point. We result in getting the y-intercept of 2.

The answer is y = 1/2x + 2

Answer 2

y =
`(1)/(2)` x + 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 + 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)` =
`(1)/(2)` , thus

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

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

3 = 1 + c ⇒ c = 3 - 1 = 2

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