Step by step
The question
Question: y varies directly with x.
y = 15 when x = 5.
Find y when x = 8.
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 = 15 and x = 5.
k times 5 is written 5k.
5k means 5 times k.
We want just k.
To remove times 5, we divide by 5.
We do it on both sides, so they stay equal.
Careful!
k is y divided by x: 15/5.
Not 5/15.
The y number goes on top.
Is k alone now?
Not yet: 5k means 5 times k.
How do we remove it?
15/5 on the left.
5k/5 on the right.
5 divided by 5 is 1.
They cancel each other.
So just k is left.
15 divided by 5 is 3.
So k = 3.
So after step 2: we divided by 5, and now we have k = 3.
3 Write the equation
We put 3 in place of k.
So the equation is y = 3x.
4 Find y
We put in x = 8.
3 times 8 is 24.
So y = 24.
5 Check
Let's check.
In direct variation, y divided by x is always k.
That is how we found k.
First pair: 15/5 is 3.
New pair: 24/8 is 3 too.
The same k.
So the answer is right!
6 Type it in
The answer box takes 5 characters.
24 has 2.
It fits.
We type 24.
Let's look back.
First: write the rule.
Then: find k.
Then: write the equation.
Then: find y.
Then: check.
Last: type it in.