Remark
You already know the slope. It is - 2
So far your answer is y = - 2x + b where b is the y intercept. Now all you need do is use the point (2, -2) to find the y intercept.
Solution
y = -2x + b
x = 2
y = - 2
-2 = -2 * 2 + b
-2 = -4 + b
-2 + 4 = b
b = 2
The answer is
y = -2x + 2 <<<< Answer.
