Question

What is the equation of the line that is perpendicular to line m and passes through the point (3,2)

Answer 1

y =
`(2)/(5)` x +
`(4)/(5)`

Explanation:

the equation of a line in slope- intercept form is

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

calculate m using the slope formula

m =
`(y_(2)-y_(1) )/(x_(2)-x_(1) )`

with (x₁, y₁ ) = (- 2, 2) and (x₂, y₂ ) = (0, - 3) ← 2 points on the line

m =
`(-3-2)/(0-(-2))` =
`(-5)/(0+2)` = -
`(5)/(2)`

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

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

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

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

2 =
`(6)/(5)` + c ⇒ c = 2 -
`(6)/(5)` =
`(10)/(5)` -
`(6)/(5)` =
`(4)/(5)`

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

Answer 2

y= 2/5x+4/5

Explanation:

identify two points on line m then find it's gradient.

using the gradient of line m find the gradient of the perpendicular line

then use points (3,2) and (x,y) to find it's equation.