Moving from (-4, -9) to (5, 3), x (the 'run') increases by 9 from -4 to 5, and y (the 'rise') increases by 12 from -9 to +3. Thus, the slope of the line connecting the two points is
m = rise / run = 12/9 = 4/3
It may help to think of the change in x (9) as the horizontal leg of a right triangle and the change in y (12) as the vertical leg. Then
m = (vertical leg length) / (horizontal leg length) = 12/9 = 4/3
this is because when 40 is broken down into two numbers (one divisible to get out of the square root, and one not) you get 25 + 15 under the square root. we know that the square root of 25 is 5, so we can put 5 outside the root and leave 15 inside.
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