First let's assume that the table contains points on a straight line. Then all we have to do is to determine the slope of that line.
Suppose we go from (0,3) to (7,-28.5).
-28.5-3 -31.5
Then the slope, m, is m = ------------- = ---------- = - 9/2, or - 4.5.
7-0 7
Let's check this result!
Suppose that y = mx + b governs the relationship between x and y.
Then y = -4.5x + b
suppose we find b by substituting the coordinates from the point (0,3):
3 = -4.5(0) + b
Then b = 3, and y = -4.5x + 3. Does the point (-2,12) satisfy this equation?
Does 12 = -4.5(-2) + 3? Does 12 = 9 + 3? YES.
So y = -4.5x + 3 is the equation from which these points came, and the rate of change of y with respect to x is the slope m = -4.5, or m = -9/2.
