Question

What is the equation of the line passing through (2, –2) and perpendicular to the line y = –x + 3 in slope-intercept form?

Answer 1

so your slope in the equation is -1. However, a perpendicular line will have a negative reciprocal of the slope. So the negative reciprocal of -1 is 1.
now lets put your info into y = mx + b using slope 1 and points (2,-2).
y = mx + b
-2 = 1(2) + b
-2 = 2 + b
-2 -2 = b
-4 = b

so your equation is y = 1x - 4 or just y = x - 4