Question

Determine the rate of change of the linear function given the table below.

x y
-3 -10
-2 -7
-1 -4
0 -1
1 2

Answer 1

To determine the rate of change of the linear function, we need to calculate the difference in the y-values divided by the difference in the x-values for any two points.

For example, using the points (-3, -10) and (-2, -7):
Rate of change = (-7 - (-10)) / (-2 - (-3))
Rate of change = (-7 + 10) / (-2 + 3)
Rate of change = 3 / 1
Rate of change = 3

Similarly, using the points (-2, -7) and (-1, -4):
Rate of change = (-4 - (-7)) / (-1 - (-2))
Rate of change = 3 / 1
Rate of change = 3

And the same for the other pairs of points, we find that the rate of change is constant and equal to 3 for this linear function.