Question

what is the rate of change simplified in fraction form?

A line passes through the points on this table

x to y

-15 to -11
-10 to -10
5 to 7
45 to 1

Answer 1

First, check the slope (rate of change) between successive points. Slope = Δy / Δx.

- From (-15, -11) to (-10, -10): slope = (-10 - (-11)) / (-10 - (-15)) = 1 / 5.
- From (-10, -10) to (5, 7): slope = (7 - (-10)) / (5 - (-10)) = 17 / 15.
- From (5, 7) to (45, 1): slope = (1 - 7) / (45 - 5) = -6 / 40 = -3 / 20.

The slopes are not the same, so these points are not all on a single line.

If you meant the overall rate of change from the first point to the last, that's (1 - (-11)) / (45 - (-15)) = 12 / 60 = 1 / 5.

Which of these did you want: the consecutive rates above, or the overall rate from first to last?