Question

What is the equation of the line that passes through the point (-6,2)(−6,2) and has a slope of -3/2?

Answer 1

Given:

A line passes through the point (-6,2) and has a slope of
`-(3)/(2)`.

To find:

The equation of line.

Solution:

If a line passes though a point
`(x_1,y_1)` and has a slope m, then the equation of line is

`y-y_1=m(x-x_1)`

The line passes through the point (-6,2) and has a slope of
`-(3)/(2)`. So, the equation of line is

`y-2=-(3)/(2)(x-(-6))`

`y-2=-(3)/(2)(x+6)`

`y-2=-(3)/(2)(x)-(3)/(2)(6)`

`y-2=-(3)/(2)(x)-9`

Add 2 on both sides.

`y=-(3)/(2)(x)-9+2`

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

Therefore, the equation of line is
`y=-(3)/(2)x-7`.