Compute y = k / x instantly. Enter values of x and k to find y and see a step-by-step solution. The graph of inverse variation is also displayed.
Inverse variation means when x increases, y decreases proportionally. Formula: y = k / x. Constant k = x × y.
This calculator helps you compute values for the inverse variation formula y = k / x. Enter either the independent variable x and constant k to find y. It also displays a graph of the function and a step-by-step calculation for better understanding.
The calculator automatically computes:
y = k / x
Just input x and k, and the result is displayed instantly.
The graph updates automatically based on the values of x and k.
Check the “Show Step-by-Step” box to see how y is calculated.
Features include:
1️⃣ Enter the independent variable x and the constant k.
2️⃣ The calculator computes:
3️⃣ The result is displayed instantly with the chosen precision.
4️⃣ The graph updates dynamically:
5️⃣ Optional step-by-step view explains the calculation:
In mathematics, an inverse variation describes a relationship between two variables where one variable increases while the other decreases proportionally. This relationship is commonly expressed with the formula:
y = k ÷ x
Here, y is the dependent variable, x is the independent variable, and k is the constant of variation. The constant k represents the product of the two variables:
k = x × y
This formula shows that no matter how x changes, the product of x and y always equals k. If x increases, y must decrease to keep the constant the same, and vice versa. Understanding this relationship is essential in fields like physics, economics, and engineering where inverse proportionality often occurs.
Example: Suppose k = 20 and x = 5. Using the formula:
(20 ÷ 5) = 4
Therefore, y = 4. The product of x and y is always k, because 5 × 4 = 20. If x changes to 10, then y becomes 2, keeping the product k constant.
Inverse variation formulas are widely used to model real-world scenarios such as:
By understanding the formulas y = k ÷ x and k = x × y, you can quickly calculate missing values, interpret graphs, and analyze how variables change inversely in practical applications.
Suppose you enter:
x = 5, k = 20
The calculator computes:
y = 20 / 5
Result:
y = 4
The graph will show the curve of y = 20 / x with the point (5, 4) highlighted.
Everything you need to know about calculating values for y = k / x, understanding inverse variation, and interpreting the results.
It calculates the value of y based on the formula y = k / x using the provided values of x (independent variable) and k (constant). It also displays a dynamic graph and provides optional step-by-step calculations.
Inverse variation describes a relationship where one variable increases as the other decreases proportionally. The formula is y = k / x, and the product x × y is always equal to the constant k.
No. x cannot be zero because division by zero is undefined. The calculator will show an error message if you try to enter x = 0.
Yes. If y and x are known, the calculator can compute k using the formula k = x × y.
The precision dropdown lets you control the number of decimal places for the displayed result. You can choose from 1 to 10 decimal places.
Yes. By checking the “Show Step-by-Step” option, you can see how the calculator identifies x and k, computes y = k / x, and formats the result based on your selected precision.
The graph dynamically plots the curve y = k / x for a range of x values. It highlights the calculated point (x, y) and adjusts the axes automatically to best display the curve.
Yes. It is completely free and works instantly without any registration or downloads.
Absolutely. The calculator is fully responsive and works smoothly on smartphones, tablets, laptops, and desktop computers.
It helps students understand inverse variation concepts, verify manual calculations, visualize the curve, and see step-by-step computations, making it a practical learning tool.
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