Question 285679
The line we are looking for is perpendicular to the given equation, which means that its slope is the negative reciprocal of the slope of the given equation.

3x + 5y = 8

5y = -3x + 8

y = (-3/5)(x) + 8

The negative reciprocal of (-3/5) is (5/3) because (-3/5) times (5/3) = -1.

We now plug (5/3) and your point (8, -6) into the point-slope formula and solve for y.

y - (-6) = (5/3)(x - 8)

y + 6 = (5/3)(x) - 40/3

y = (5/3)(x) - 40/3 - 6

y = (5/3)(x) - 22/3