Thank you for the opportunity to help you with your question!
So the standard equation of a line is y = mx + b where m is slope, and b is the y-intercept.
To find the slope of the line you use the equation (y2 - y1) / (x2 - x1) where (0, -2) is (x1, y1) and (-2, -6) is (x2, y2).
So first you subtract: (-6 - -2) since two negatives make a positive it's (-6 +2) which is -4
Then you subtract the x's: (-2 - 0) which is just -2
Now that you have the numbers you divide: -4/-2 Dividing with two negative numbers makes a positive so you get +2 or just 2. That is the slope of the line or m.
so now you have y = 2x + b
To find the b value you plug one of the points into the equation for y and x. Using (0, -2) where 0 is x and -2 is y we get: -2 = 2(0) + b .. Since 2 x 0 is 0, then b is equal to -2. So your final line equation is
y = 2x -2
Please let me know if you need any clarification. I'm always happy to answer your questions.