I am really having issues with the slope intercept equations and would like your assisance with the below question:

Question

The line through (2,-3) that is perpendicular to the line 5x + 3y = 9
Thank you,

Answer 1

Given line 5x  + 3y  = 9

Subtract 5x  from each side.

5x  - 5x  + 3y = 9 - 5x

3y  = 9 - 5x

Divide each side by  3.

3y /3 = (9-5x )/3

y  = 3 - 5x /3

y  = - 5x /3 + 3

Compre it to slope intercept form of a line y  = mx + b .

Slope = -5/3.

We know that perpendicular lines slope are negitive reciprocal to each other.

Slope of the perpendicular line = 3/5.

Perpendicular line passes through (2 , -3).

Equation of line in point slope form is 

Cross multiplication.

5y  + 15 = 3x  - 6

Subtract 15 from each side.

5y  = 3x  - 21.

Divide each side by 5.

Required line equation y  = 3x /5 - 21/5.