Free · Algebra
Direct Variation: Constant and Values
Find the constant of direct variation or a missing x or y in y=kx, with a sampled straight-line chart.
- Formula & worked example
- Private in your browser
- No signup
Calculator inputs
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How to use this calculator
- Enter the known values in the units shown. Results update as you type.
- Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
- Use the worked example to check the method. Reset restores the starting fields.
Private by default
Inputs and results stay in this browser tab. Bookify does not upload or store the values you enter.
Formula and method
If k=3 and x=4, y=12. Keeping k fixed makes y scale in direct proportion to x.
y=kx; k=y/x; x=y/k when k≠0.
Worked example
Enter these known values and leave the other values blank.
- Direct proportionality constant (k)
- 3
- Independent variable (x)
- 4
- Dependent variable (y)
- 12
Assumptions and limitations
- All three original numerical controls are editable and unitless. Use one consistent interpretation for x and y; the proportionality constant carries any resulting unit ratio.
- The captured workflow excludes x=0. Mathematically y=kx is defined there, but y=0 at x=0 cannot determine k. This tool preserves that original nonzero-x input contract.
- The captured extension allows a zero constant (the cited textbook defines direct variation with nonzero k): every permitted nonzero x gives y=0. Entering k=0 and y=0 alone cannot recover a unique x; k=0 with nonzero y is inconsistent.
- The chart retains eleven samples from x−5 through x+5 at integer offsets and uses ordinary browser plotting precision. It is an illustration; the numeric controls use 64 significant digits. A nonzero input or sample that would be lost to zero, or a nonfinite sample, makes the chart unavailable with an explicit notice. Valid scalar results remain available independently.
- Supported decimal/scientific inputs must be exactly representable by the existing bounded finite-input proof. Nonzero inputs below 10^-10000 are outside its working range. Clearing unknowns avoids redundant constraints; conflicting locked values are rejected.
Common questions
How do I find the constant of variation?
Divide a known y by its corresponding nonzero x: k=y/x. For y=18 and x=6, k=3.
Can the constant be negative or zero?
Yes. Negative k reverses the sign of x; k=0 gives y=0 for every permitted x. Two zero values k and y do not determine x uniquely.
Does direct variation include an added constant?
No. A relation y=kx+b with nonzero b is linear but is not direct variation because it does not pass through the origin.
References
Bind the original eleven-point direct-variation chart to its entire captured callback and source; preserve all three controls and inverse formulas. Replace approximate nonzero comparison with an exact sign predicate and bind the existing finite-input/scientific display policy to the complete source/schema.