As we're given a point on the line and the slope of the line, use the "point-slope" formula for the equation of a straight line:
y = mx + b
Here everything is known except for the slope, m. Substitute -2 fpr b, -4 for y and 2 for x:
-4 = m(2) - 2. Adding 2 to both sides of the equation, we get
-2 = 2m, and thus m = -1.
The desired equation is y = -x - 2.
