Calculator

Proportional Relationship Calculator with Steps

Solve proportional relationship problems, find missing values, and see step-by-step explanations with examples.

y = kx

The constant of proportionality k relates y to x

Enter two points (x, y) from a table or graph to find k.

x₁

y₁

x₂

y₂

How to use this calculator

Enter any two pairs of values from a proportional relationship. The calculator finds the constant of proportionality k and solves for any missing value using the equation y = kx.

What this means in math class

In 7th-grade math, proportional relationships appear as tables, graphs, and equations. This calculator helps verify your work and shows every step so you can check your understanding.

Worked examples

Example 1: Find k from a table

x = 2, y = 10 and x = 5, y = 25

Step 1:Divide y₁ by x₁: 10 ÷ 2 = 5
Step 2:Divide y₂ by x₂: 25 ÷ 5 = 5
Step 3:Both ratios equal 5, so k = 5
Step 4:The equation is y = 5x

Answer: k = 5, y = 5x (proportional)

Example 2: Find a missing value

y = 4x, find y when x = 7

Step 1:The equation is y = 4x
Step 2:Substitute x = 7: y = 4 × 7
Step 3:y = 28

Answer: y = 28

Example 3: Check if two ratios form a proportion

Is 3/4 = 9/12?

Step 1:Cross multiply: 3 × 12 = 36
Step 2:Cross multiply: 4 × 9 = 36
Step 3:Both products equal 36
Step 4:Yes, these ratios form a proportion

Answer: Yes — 3:4 and 9:12 are proportional

Frequently asked questions

What is a proportional relationship?

A proportional relationship is one where two quantities always change at the same rate, written as y = kx where k is the constant of proportionality.

How do you find the constant of proportionality?

Divide y by x for any pair of values. The result is k.

Can k be a fraction?

Yes. k can be any real number — whole number, fraction, or decimal.

What if my table has negative values?

The same method works. Divide y by x and compare the ratios.

Does the graph have to go through zero?

Yes. In a proportional relationship y = kx, when x = 0, y must equal 0.

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