How To Find The Line Of Altitude In A Triangle

I'm having trouble with this:

Triangle UVW has the following vertices. Write the equation of the line of the altitude through U.

U(5, 8), V(3, 7), W(8, 2)

Fact: the altitude of UVW through U is perpendicular to VW
Fact: the slope of a line is the negative reciprocal of the slope of a perpendicular to it

The slope of VW is (change in y) / (change in x) = (7 - 2) / (3 - 8) = 5 / (-5) = -1

The slope of the altitude is the negative reciprocal of that, -1/m = -1/(-1) = 1

Find an equation for the line with slope 1 through the point (5,8) = U

(y-8) = 1 (x-5)

y = x + 3 FINAL ANSWER.