Pencils: 3 → $6, 5 → $10, 7 → $14
A store sells pencils. The more you buy, the more it costs. Let's find the secret number that links them.
Here's our data. Three pencils cost six dollars, five cost ten, seven cost fourteen.
To find the constant of proportionality, we'll divide y by x for every row.
Six divided by three equals two.
Ten divided by five also equals two.
Fourteen divided by seven? Two again!
Every row gives the same answer. That sameness is what makes it proportional.
We call that number k, the constant of proportionality. Here, k equals two.
So our equation is y equals two x. Cost equals two times the number of pencils.
In real life, k means each pencil costs two dollars. That's the unit price!
The constant of proportionality is two dollars per pencil. You found k!