Question

What is the equation of the line that is perpendicular to the given line and passes through the point (3, 0)?

3x + 5y = −9

3x + 5y = 9

5x − 3y = −15

5x − 3y = 15

Answer 1

I did this last year if i remember it was 5x − 3y = 15

Answer 2

5x - 3y = 15

Explanation:

Given line has two points (-3,2) and (3,0)

Now we find the slope of given line

`slope m = (y_2-y_2)/(x_2-x_1) =(-1-2)/(2+3) =(-3)/(5)`

Slope of given line is -3/5

Slope of perpendicular line is the negative reciprocal of the slope of given line

slope of perpendicular line =
`(5)/(3)`

It passes through the point (3, 0)

We know the slope and the point (3,0), so we use point slope form

`y-y1= m(x-x1)`

`y - 0 = (5)/(3)(x-3)`

`y= (5)/(3)x-5`

Now we multiply the whole equation by 3

3y = 5x - 15

Subtract 5x on both sides

-5x + 3y = -15

Divide the whole equation by -1

5x - 3y = 15