Step by step
The question
Question: y is directly proportional to x.
y = 36 when x = 9.
Find y when x = 2.
1 Write the rule
Varies directly means y is always the same number times x.
When x gets bigger, y gets bigger too.
We call the number k: y = kx.
k stays the same for every pair of numbers.
Books call it the constant of variation.
2 Find k
We put in y = 36 and x = 9.
k times 9 is written 9k.
9k means 9 times k.
We want just k.
To remove times 9, we divide by 9.
We do it on both sides, so they stay equal.
Careful!
k is y divided by x: 36/9.
Not 9/36.
The y number goes on top.
36/9 on the left.
9k/9 on the right.
9 divided by 9 is 1.
So just k is left.
36 divided by 9 is 4.
So k = 4.
3 Write the equation
We put 4 in place of k.
So the equation is y = 4x.
4 Find y
We put in x = 2.
4 times 2 is 8.
So y = 8.
5 Check
Let's check.
In direct variation, y divided by x is always k.
First pair: 36/9 is 4.
New pair: 8/2 is 4 too.
The same k.
So the answer is right!
Let's look back.
First: write the rule.
Then: find k.
Then: write the equation.
Then: find y.
Last: check.