Question 785081
y = mx + b is the slope intercept form of a line equation.  m is the slope.  Parallel lines have the same slope.<P>
y=-x+3 the slope is -1.  So the slope of the parallel line is also 1.<P>
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.<P>
So the equation of this parallel line is y - (-2) = -1(x-(-2) which is y+2 = -x-2<P>
We can write this in the slope intercept form by subtracting 2 from both sides.<P>
y = -x - 4<P>
{{{ graph( 300, 200, -6, 5, -10, 10, -x-2, -x-4) }}}