Constant of proportionalityConstant and equation
Name: Date:
Do what each table asks — find the constant, or write the equation.
1x2589y246096108y =x
2x4689y8121618y =x
3x2679y22667799k
4x4578y40507080k
5x2567y6151821k
6x4578y16202832k
Constant of proportionality worksheets
In a proportional table one number turns every x into its y. These free printable worksheets ask for that constant — read straight off the table, or written into the equation y = kx.
Kid stuck on one? You don’t just get the sheet.
Constant of proportionality
The answer key prints on a separate page.
What's on this sheet
The constant of proportionality is a unit rate wearing a letter. On a table where 2 buys 24 and 5 buys 60, the constant is 12 — the amount for one — and every column confirms it. Finding it is a division, y ÷ x, and the sheet is built so it always comes out a whole number: the structure stays visible while the idea lands.
Why this sheet works
Every table here is proportional, which means it passes through the origin — double the x and the y doubles too, and y ÷ x is the same in every column. That is the year-seven idea that year eight then generalises: a line that need not start at zero. Checking a second column, not just the first, is the habit the sheet trains, because a table is only proportional if the constant holds all the way across.
How this one works
One question from this sheet, worked through a step at a time.
x: 2, 5, 8, 9 y: 24, 60, 96, 108
x2589y246096108
24÷2=12
60÷5=12
y=12x
- In a proportional table every y is its x times the SAME number — the constant of proportionality. Find it by dividing a y by its own x.
- Take the first column: 24 ÷ 2 = 12.
- Check another column so it is not a fluke: 60 ÷ 5 = 12. Every column gives 12, so the constant is 12.
- So the equation is y = 12x — it says "each y is x times 12".