Step by step
The question
Question: y varies directly with x.
y = 20 when x = 5.
Write the equation.
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 = 20 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: 20/5.
Not 5/20.
The y number goes on top.
20/5 on the left.
5k/5 on the right.
5 divided by 5 is 1.
So just k is left.
20 divided by 5 is 4.
So k = 4.
3 Write the equation
We put 4 in place of k.
So the equation is y = 4x.
4 Check
Let's check with the pair we know: put in x = 5.
We get 20, like in the question.
So the equation is right!
Let's look back.
First: write the rule.
Then: find k.
Then: write the equation.
Last: check.