y=-x+3 the slope is -1. So the slope of the parallel line is also 1.

y - y(1) = m(x-x(1)) is the point slope form of a line equation where (x(1),y(1)) is a point on the line, and m is the slope.

So the equation of this parallel line is y - (-2) = -1(x-(-2) which is y+2 = -x-2

We can write this in the slope intercept form by subtracting 2 from both sides.

y = -x - 4