Question

Aline passes through (-3,-2) and is perpendicular to 3x - 2y = 7.

What is the equation of the line in slope-intercept form?

Answer 1

y = -
`(2)/(3)` x - 4

Explanation:

The equation of a line in slope- intercept form is

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

Rearrange 3x - 2y = 7 into this form by subtracting 3x from both sides

- 2y = - 3x + 7 ( divide all terms by - 2 )

y =
`(3)/(2)` x -
`(7)/(2)` ← in slope- intercept form

with slope m =
`(3)/(2)`

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

`m_(perpendicular)` = -
`(1)/(m)` = -
`(1)/((3)/(2) )` = -
`(2)/(3)`, thus

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

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

- 2 = 2 + c ⇒ c = - 2 - 2 = - 4

y = -
`(2)/(3)` x - 4 ← equation of perpendicular line

Answer 2

y=
`-(2)/(3)`x-4

Explanation:

3x-2y=7

-3x -3x

-2y=-3x+7

/-2 /-2

y=
`(3)/(2)`x-
`(7)/(2)`

perpendicular lines always have opposite reciprocal slopes

3/2--> -2/3

y=-2/3x+b

-2=-2/3(-3)+b

-2=2+b

-2 -2

b=-4

y=-2/3x-4