To calculate the rate of change, you follow these steps.
Step 1: Display the points given inside of an array. In this case, our points are (2,6), (3,11), and (4,16).
Step 2: Find the difference between x-values and y-values respectively.
For x values, the differences are as follows:
- The difference between 3 and 2 is: 3 - 2 = 1
- The difference between 4 and 3 is: 4 - 3 = 1
For the y values, the differences are as follows:
- The difference between 11 and 6: 11 - 6 = 5
- The difference between 16 and 11: 16 - 11 = 5
Step 3: The rate of change between two points is the difference in the y-coordinates divided by the difference in the x-coordinates.
Let's find the rate of change:
rate of change between points (2,6) and (3,11):
rate = (Δy / Δx) = 5/1 = 5
rate of change between points (3,11) and (4,16):
rate = (Δy / Δx) = 5/1 = 5
So, the rate of change is 5 for both pairs of points, meaning the change in y for each unit change in x is constant, which is characteristic of a linear relationship between x and y.