Answer:
y = -5/3x + 3
Explanation:
First lets turn the equation from standard form to slope intercept form.
3x - 5y = 1
~Subtract 3x to both sides
-5y = 1 - 3x
~Divide -5 to everything
y = -1/5 + 3/5x
~Reorder
y = 3/5x - 1/5
Now that we have the equation in slope intercept form, we can find the new equation. A perpendicular line will have the opposite reciprocal of the original slope.
3/5x -> -5/3x
Now that we have the slope, we can use the given point to find the y-intercept.
y = -5/3x + b
8 = -5/3(-3) + b
8 = 5 + b
3 = b
Put all the information we solved for into a final equation.
y = -5/3x + 3
Best of Luck!