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
