Directions: Using the digits 1 to 9 at most one time each, fill in the boxes to create a table of values that represent a linear function.

### Hint

What has to happen for a table to show a linear relationship? What has to happen for a table to NOT show a linear relationship?

### Answer

Here are two possible solutions. The first number is the x-value and the second number is the y-value.

Solution 1

1 2

3 4

5 6

7 8

Solution 2

1 5

2 6

3 7

4 8

Source: Robert Kaplinsky

Can we swap x and y and create two more solutions?

You most certainly can, in fact it’s quite encouraged.

x:y

1:3

2:7

3:7

4:4

7:1

5:7

Using digits 1 through 4 at most once each, there are 9 different ways to complete the tables to create a table of values that represents a linear function.

https://twitter.com/PuntMat/status/1102466314399039488

x y

1 1

2 3

3 6

4 9

X Y

12:14

14:15

16:16