Write the Equation of the line that pass through the point 2

Write the Equation of the line that pass through the point (-2, 3) and that is perpendicular to the line 3x -5y = 4. Write your final answer using the general form

Solution

Given line is:

3x - 5y = 4

5y = 3x - 4

y = 3x/5 - 4/5

Slope of this line is 3/5

Slope of a perpendicular line is -5/3 as M1 * M2 = -1 where M1 and M2 are slopes

So, new line is

y = -5x/3 + c which passes through -2,3

3 = 10/3 + c

c = -1/3

So, equation is:

y = -5x/3 - 1/3