You did almost everything correctly. You found the right slope and plugged it back into the equation which should look like y-(-2)=-4/3(x-5) There should be parenthesis around the (x-5). When you continue solving, you will get a positive 20 (the -4/3 and the -5 cancel out) so you will end up with 14 on the right side of the equation. If you plug your given point (5,-2) back in, it will check out :)
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What are coordinates of the given point? P95, -20 or P(5,-2)?