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Is it proportional: x 2, 3, 5; y 6, 9, 16

Step by step, with the reason for every step · Proportional relationships · Foundations

Step by step

The question

Question: is this table proportional: x is 2, 3, 5, and y is 6, 9, 16?

x: 2, 3, 5; y: 6, 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.

6/2 is 3.

9/3 is 3.

16/5 is 3.2.

= 62 = 3, 93 = 3, 165 = 3.2

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!

6 ÷ 2 ≠ 9 ÷ 3

Let's look back.

First: divide y by x.

Then: compare the answers.

Last: check.

Answer
= not the same → not proportional

Your turn

Try this one yourself, then check:

Is this table proportional: x: 2, 3, 5; y: 11, 15, 23
Show the answer
not proportional

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