Direct Variation Calculator
Solve y=kx direct variation problems. Enter a known (x1,y1) pair to find k, then compute y at any new x. Covers proportional-relationship algebra problems.
How to use this tool
- Enter known x1, known y1 and new x2 in the fields above.
- Results update instantly as you type — or click Calculate.
- Read your new y2 and the full breakdown beneath it.
Formula
k = y1 / x1; y2 = k * x2
How it works
Divide the known y by the known x to get k, then compute the new y: y2 = k × x2.
Worked example
y=12 when x=4; find y when x=7
- k = 12/4 = 3
- y2 = 3*7 = 21
Common mistakes to avoid
- Using an x1 value of zero to find k, which makes k undefined since division by zero is not allowed.
- Confusing direct variation (y=kx) with inverse variation (y=k/x); in direct variation y increases as x increases.
- Computing k from one pair and then forgetting to use the same k for the new x, effectively creating a different proportional relationship.
Key terms
Frequently asked questions
- How do I know if a relationship is direct variation?
- Compute y/x for each pair. If the ratio is constant and the line passes through the origin, the relationship is direct variation.
- What does the constant of variation k represent?
- k is the rate of change: for every one-unit increase in x, y increases by k. It is the slope of the line y = kx through the origin.
- What is the difference between direct variation and slope-intercept form?
- Direct variation is a special case of y = mx + b where b = 0. A non-zero y-intercept means the relationship is not direct variation.