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When a set of data represents a linear function, the rate of change is constant. Create a table which supports your claim, then rearrange it to have a table which supports your friend's claim.
Example solution:
Your Claim
| x | y |
|---|---|
| -4 | 1 |
| -3 | 2 |
| -2 | 3 |
| -1 | 4 |
Friend's Claim
| x | y |
|---|---|
| -4 | 2 |
| -3 | 1 |
| -2 | 3 |
| -1 | 4 |
Let's choose the values to support our claim first, then we will rearrange them to support our friend's claim. Keep in mind that these are just one possible answer for this problem.
Since the increase is linear in both rows, let's choose the first 4 top tiles as our x-values and the first 4 bottom tiles as the y-values.
| x | y |
|---|---|
| -4 | 1 |
| -3 | 2 |
| -2 | 3 |
| -1 | 4 |
When x increases by 1 the value of y increases by 1. Therefore, this is a linear function.
Our friend wants to create a table of values that represents a nonlinear function. This means that the rate of change will not be constant. To do this, we can exchange 2 of the y-values from the table that supported our claim. Let's switch y=1 with y=2.
| x | y |
|---|---|
| -4 | 2 |
| -3 | 1 |
| -2 | 3 |
| -1 | 4 |
Now the rate of change is not constant, so it is a nonlinear function.
