Question

Equation perpendicular to y=-2x+5 and goes through point (-3,4)

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 + 5 ← 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 (- 3, 4) into the partial equation

4 = -
`(3)/(2)` + c ⇒ c = 4 +
`(3)/(2)` =
`(11)/(2)`

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