Calculator
Example Data Table
| Known x | Known y | k = y / x | Target x | Target y |
|---|---|---|---|---|
| 4 | 20 | 5 | 9 | 45 |
| 3 | 12 | 4 | 7 | 28 |
| 8 | 2 | 0.25 | 20 | 5 |
Formula Used
k = y / x
x = y / k
Direct variation means one value changes by the same constant factor as another value. In the equation, k is the constant of variation. If every pair has the same y / x ratio, the relationship is direct variation.
How to Use This Calculator
Enter a known x and known y to calculate the constant. You may also enter k directly. Then enter a target x to find y, or enter a target y to find x. Use the optional table fields to build a sequence of proportional pairs. Add extra pairs in the checker to test whether they match the same constant. Press calculate, then review the result above the form. Use the CSV or PDF buttons to save your work.
Direct Variation Guide
What Direct Variation Means
Direct variation describes a proportional relationship between two quantities. When x grows, y grows by a fixed multiplier. When x shrinks, y shrinks by the same rule. The equation is simple. It is y = kx. The letter k is the constant of variation. It tells how many y units belong to each x unit.
Why the Constant Matters
The constant is the key value. It connects every pair in the relationship. If x is 4 and y is 20, then k is 5. That means each x unit gives five y units. The equation becomes y = 5x. You can now predict any matching value.
Checking Proportional Pairs
A direct variation table must keep the same ratio. Divide each y value by its x value. Every valid pair should return the same k. If one ratio changes, the table is not perfectly proportional. This calculator checks those pairs for you. It also marks values that do not match.
Using the Calculator for Study
This tool supports several common algebra tasks. You can find k from one pair. You can solve y from x. You can solve x from y. You can also create a table for graphing practice. The generated equation helps students see the rule clearly. The export buttons are useful for homework records.
Graph Meaning
Direct variation graphs form straight lines. The line passes through the origin. A larger k makes the line steeper. A smaller k makes it flatter. Negative k values slope downward. This link between equation, table, and graph makes direct variation easy to compare.
FAQs
1. What is direct variation?
Direct variation is a relationship where y equals k times x. The ratio y divided by x stays constant for every valid pair.
2. How do I find the variation constant?
Divide y by x. For example, if x is 4 and y is 20, then k equals 5.
3. Can x be zero?
x cannot be zero when calculating k with y divided by x. Division by zero is undefined, so another valid pair is needed.
4. What does y = kx mean?
It means y changes directly with x. The value k controls the size and direction of that change.
5. How can I find y from x?
Multiply the x value by k. For example, with k equal to 5 and x equal to 9, y equals 45.
6. How can I find x from y?
Divide y by k. This works when k is not zero. The calculator shows the step in the result section.
7. How do I check a table?
Divide each y value by its matching x value. If all ratios are equal, the table shows direct variation.
8. Can I download my result?
Yes. After calculation, use the CSV or PDF button to save the equation, steps, table, and pair checks.