how does the rate of change vary from point to point?
X Y
40 32
28 16
16 12
To determine how the rate of change varies from point to point, you can calculate the difference in the values of Y divided by the difference in the values of X for each pair of points.
Let's calculate the rate of change for the given points:
For the first pair of points (40, 32) and (28, 16):
Rate of change = (Y2 - Y1) / (X2 - X1)
= (16 - 32) / (28 - 40)
= -16 / -12
= 4/3
For the second pair of points (28, 16) and (16, 12):
Rate of change = (Y2 - Y1) / (X2 - X1)
= (12 - 16) / (16 - 28)
= -4 / -12
= 1/3
So, as you can see, the rate of change varies between 4/3 and 1/3 from point to point.
To understand how the rate of change varies from point to point, we can calculate the average rate of change between adjacent points. The average rate of change represents the amount of change in the dependent variable (Y) for each unit change in the independent variable (X).
Let's calculate the average rate of change between the first two points (40, 32) and (28, 16):
Change in Y = 16 - 32 = -16
Change in X = 28 - 40 = -12
Average rate of change = Change in Y / Change in X
Substituting the values:
Average rate of change = -16 / -12 = 4/3 or 1.33
For the next set of points (28, 16) and (16, 12):
Change in Y = 12 - 16 = -4
Change in X = 16 - 28 = -12
Average rate of change = -4 / -12 = 1/3 or 0.33
Thus, we can see that the rate of change varies from point to point. In the given dataset, the average rate of change between the first two points is 1.33, while it is 0.33 between the last two points. This indicates that the rate of change is increasing as we move from (28, 16) to (40, 32) and decreasing as we move from (16, 12) to (28, 16).