Question

How do you find the slope of a line perpendicular to `2x+3y=5`?

Answer 1

If you call the slope of your line `m` the slope of the line perpendicular to it will be: `m_1=-1/m`
Your line can be written in the form `y=mx+b` isolating `y` on one side as:
`y=-2/3x+5/3`
The slope will then be: `m=-2/3`
The slope of the perpendicular will then be: `m_1=-1/m=3/2`