Proportional Relationships: Tables, Graphs and Equations

What you will learn

Two quantities are proportional when one is always a constant multiple of the other. If y is proportional to x, the relationship can be written y = kx, where k is the constant of proportionality. This lesson shows how the same relationship appears in a table, on a graph, and in a real-world statement. Careful attention to zero and to units prevents common mistakes.

Core ideas

• In a proportional table, the ratio y/x is the same for every row where x is not zero.
• A proportional graph is a straight line through the origin because x = 0 gives y = 0.
• The constant k is a unit rate; its units should be written and interpreted in context.
• A straight line that does not pass through the origin is linear but not proportional.

A practical way to use this resource

1. Compute y/x for at least three table rows and compare the results.
2. Write the equation y = kx using the shared ratio.
3. Plot the ordered pairs and verify that the line would pass through (0,0).
4. Use the equation to predict a new value, then state what k means with units.

Check your understanding

A recipe uses 6 cups of water for 2 cups of rice. The ratio is 3 cups of water per cup of rice, so w = 3r. Predict the water for 5 cups of rice and explain why adding a fixed amount instead would not model a proportional relationship.

Accuracy and next steps

Use this page as a learning guide, compare your work with course requirements, and ask an instructor when a local rule or assignment direction differs.