We know that the slope intercept formula is y = mx+b
We also know that when x is zero, the coordinate gives us the y-intercept (which is "b"). Therefore, (0, -2) tells us directly that the b is -2. Then we need to find the slope. We can use the the slope formula, which is Y2 - Y1/X2-X1 (0-2/2-0 = -2/2 = -1). Using the formula, we determine the slope (m) is -1. With that known information, we can conclude that the slope intercept equation is y = -x - 2
Hope this helps :)