Question

What is the equation in slope-intercept form of the line that passes through the point (2,-2) and is perpendicular to the line represented by y = 2/5 x + 2

Answer 1

y = -
`(5)/(2)` x + 3

Explanation:

The equation of a line in slope- intercept form is

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

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

with slope m =
`(2)/(5)`

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

`m_(perpendicular)` = -
`(1)/(m)` = -
`(1)/((2)/(5) )` = -
`(5)/(2)`, thus

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

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

- 2 = - 5 + c ⇒ c = - 2 + 5 = 3

y = -
`(5)/(2)` x + 3 ← equation of line