Constant of proportionalityWriting y = kx
Name: Date:
Write the equation for each table in the form y = kx.
1x2346y8121624y =x
2x3469y12162436y =x
3x2369y18275481y =x
4x4579y20253545y =x
5x2479y18366381y =x
6x2456y22445566y =x
Writing y = kx worksheets
Once the constant of proportionality is known, the whole relationship fits in one short equation: y = kx. These free printable worksheets ask a child to find the constant from a table and write that equation.
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Writing y = kx
The answer key prints on a separate page.
What's on this sheet
The equation is the constant with x beside it, and seeing that is the point. If 2 buys 24 and 5 buys 60, the constant is 12, so the rule is y = 12x — no extra step, just the constant written into the form. A child who can find k from a table already has everything the equation needs; writing it down is naming what they found.
Why this sheet works
Every table is proportional, which means the line passes through the origin: double the x and the y doubles, and y ÷ x is the same in every column. That is why the equation has no constant added on the end — y = 12x, never y = 12x + 3. The year-eight leap to a line that need not start at zero is exactly the piece this stops short of.
How this one works
One question from this sheet, worked through a step at a time.
x: 2, 3, 4, 6 y: 8, 12, 16, 24
x2346y8121624
8÷2=4
12÷3=4
y=4x
- 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: 8 ÷ 2 = 4.
- Check another column so it is not a fluke: 12 ÷ 3 = 4. Every column gives 4, so the constant is 4.
- So the equation is y = 4x — it says "each y is x times 4".