Open Middle®
Directions: Using the digits 1 to 9, at most one time each, place a digit in each box 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
X: 1, 3, 5, 7
Y: 2, 4, 6, 8