Every question is the same two steps: use the pair you are given to find the constant, then use the constant on the new value. Direct means y = kx, inverse means y = k over x.
If y varies directly with x and y=12 when x=3, find y when x=7
Direct variation means y = kx.
12 = k times 3, so k = 4.
Now y = 4 times 7.
The answer is 28.
Where students go wrong
Scaling y by the same factor as x without finding the constant. That works for direct variation and fails completely for inverse, where doubling x halves y. Finding k first works for both.
Also called constant of variation, proportional relationships or y varies directly with x.
What you can put on this worksheet
Direct variation
If y varies directly with x and y=30 when x=5, find y when x=1→ 6
Inverse variation
If y varies inversely with x and y=4 when x=5, find y when x=2→ 10
Questions about these worksheets
Yes. Every direct and inverse variation sheet is free to print and free to download as a PDF. There is no account to make, no email to hand over and no limit on how many you take.
Yes. The answer key prints on a second page, and you can choose whether it shows each question beside its answer or just the answers in a list.
Yes. Print straight from the page, or download the PDF and print that. The sheet is laid out for paper rather than squeezed off a screen, so there is room to work under each question, and the answer key comes out on its own page.
Algebra 1 is usually taken around 8th or 9th grade, though schools vary and plenty of students meet it earlier or later. Pick the difficulty rather than the grade: the easy level suits a first lesson on it, the hard level suits review before a test.
Yes, as many as you like. The questions are built fresh each time rather than picked from a fixed set of files, so pressing Generate gives a new sheet. That is what you want for a second class, a retake, or two students sitting next to each other.
That is the closest comparison, and Kuta Software is good software. It is also paid software you install on a computer. These worksheets run in a browser tab for free, with no account and nothing to install. Like Kuta, the direct and inverse variation questions are generated when you ask for them rather than pulled from a fixed set of files, so two classes never get the same sheet, and the answer key comes with it.
Yes. There are three levels, and you can tick more than one for a sheet that mixes them, in which case the questions come out easiest first. The harder levels are not just larger numbers: they ask for something the easy ones do not.
You pick from 2: direct variation and inverse variation. Tick as many as you want and set how many of each, or let it spread them evenly.
Scaling y by the same factor as x without finding the constant. That works for direct variation and fails completely for inverse, where doubling x halves y. Finding k first works for both.