Find the equation of a line that passes through the point (4,2) that is perpendicular to the line y = x. show your work.

If it has to be perpedicular to y = x, then the slope has to be -1/x because perpedicular slope is the opposite reciprocal. Now plug what you know into the point slope formula. 

y - 2 = -1/1 (x - 4)

Since -1/1 is the same as -1, it can be rewritten as -1.

y - 2 = -1 (x - 4)

Now distribute -1 times x and -4.

y - 2 = -x + 4

Add 2 to both sides to get y by itself. 

y = -x + 2

Your answer should be:

y = -x + 2