Step by step
The question
Question: is this table proportional: x is 1, 2, 3, 4, and y is 1, 4, 9, 16?
x: 1, 2, 3, 4; y: 1, 4, 9, 16
Proportional means: y divided by x is always the same number.
We call that number k.
Then y = k times x.
proportional: y ÷ x is always the same
k = y ÷ x, y = kx
We write it as a table.
1 Divide y by x
For each pair we work out y divided by x.
1/1 is 1.
4/2 is 2.
9/3 is 3.
16/4 is 4.
= 11 = 1, 42 = 2, 93 = 3, 164 = 4
2 Compare the answers
The answers are not the same.
So it is not proportional.
= not the same → not proportional
3 Check
Let's check: the first two pairs already give different answers.
So the answer is right!
1 ÷ 1 ≠ 4 ÷ 2
Let's look back.
First: divide y by x.
Then: compare the answers.
Last: check.
Answer
= not the same → not proportional