Question

Find the equation of the line which passes through the point

(6, -10)and is perpendicular to the line 5X plus 3Y equals 2Y -3

Answer 1

`y= (1)/(5)x- (56)/(5)`

Explanation:

We want to find the equation of the line that goes through: !6,-10) and is perpendicular to the line

`5x + 3y = 2y - 3`

Let's simplify the equation of the line to get:

`3y - 2y = - 5x + 3`

`y = - 5x + 3`

The slope of this line is -5.

The perpendicular to this line has a slope of

`(1)/(5)`

The equation going through (6,-10) is

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

We substitute to get;

`y= (1)/(5) (x-6) - 10`

Expand;

`y= (1)/(5)x- (6)/(5) - 10`

`y= (1)/(5)x- (56)/(5)`