The rate of change, or slope, is the change in y over change in x. To find the slope, pick two points. The slope will be the change in y-coordinates over the change in x-coordinates.
As an equation, this is
[tex]slope = \frac{(y2-y1)}{(x2-x1)} [/tex]
To find the slope for function 1, pick any two points (x,y) in the table.
Let's choose (-1, 3) and (-2, 5).
The slope is
[tex] \frac{5-3}{-2+1} = \frac{2}{-1} = -2[/tex].
Let's choose (-1, 0) and (0, 4) for the two points for function 2.
The slope is
[tex] \frac{4-0}{0+1} = \frac{4}{1} = 4[/tex].
You want to compare the magnitude (without negatives) of the slope when comparing the greater rate of change/slope. In other words, you take the absolute value of each slope.
The magnitude of function 1's slope is 2.
The magnitude of function 2's slope is 4.
