Question

Find an equation in slope intercept form for the line through point P(-3, 2) and perpendicular to the line

containing the two points (2, 3) and (1, -2).​

Answer 1

see explanation

Explanation:

We require to find the slope m of the line joining the 2 given points

To find m use the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (2,3) and (x₂, y₂ ) = (1, - 2)

m =
`(-2-3)/(1-2)` =
`(-5)/(-1)` = 5

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

`m_(perpendicular)` = -
`(1)/(m)` = -
`(1)/(5)`

The equation of a line in slope- intercept form is

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

y = -
`(1)/(5)` x + c ← is the partial equation of the perpendicular line

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

2 =
`(3)/(5)` + c ⇒ c =
`(7)/(5)`

y = -
`(1)/(5)` x +
`(7)/(5)` ← perpendicular equation