Step by step
The question
Question: 2 notebooks cost $5, and 6 cost $15: is the cost proportional to the number of notebooks?
2 notebooks: $5, 6 notebooks: $15
Let x be the number of notebooks.
Let y be the cost.
x = notebooks, y = cost
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
1 Divide y by x
For each pair we work out y divided by x.
5/2 is 2.5.
15/6 is 2.5.
= 52 = 2.5, 156 = 2.5
2 Compare the answers
The same number every time.
So it is proportional, and k = 2.5.
= always 2.5 → proportional
3 Write the equation
y = k x, with k = 2.5.
So the equation is y = 2.5x.
= y = 2.5x
4 Check
Let's check: k times x should give each y.
2.5 times 2 is 5.
2.5 × 2 = 5
2.5 times 6 is 15.
So the answer is right!
2.5 × 6 = 15
Let's look back.
First: divide y by x.
Then: compare the answers.
Then: write the equation.
Last: check.
Answer
= y = 2.5x