Proportional Relationships
Grade 7 · Math · Study Guide
Learn how two quantities relate proportionally and how to identify, write, and graph proportional relationships.
A proportional relationship is one where two quantities always have the same ratio. That fixed ratio is called the constant of proportionality, usually written as k, and the relationship is expressed as y = kx. So if bananas cost $0.30 each, the equation is y = 0.30x — no matter how many you buy, the price per banana never changes.
You can spot a proportional relationship in a table by dividing each y-value by its x-value. If you always get the same number, you have a proportional relationship. If even one pair gives a different ratio, it is not proportional. This check is called verifying the constant ratio.
On a coordinate graph, a proportional relationship forms a perfectly straight line that always passes through the origin, the point (0, 0). This matters because when x is 0, y must also be 0 — if you buy zero items, you pay nothing. Any straight line that does not cross through the origin is linear but not proportional.
Proportional thinking shows up constantly in the real world. When a recipe is doubled, every ingredient doubles — that is a proportional relationship. Exchange rates, fuel efficiency, and map scales all work the same way. Knowing how to set up and solve proportions lets you tackle these problems quickly.
The equation y = kx is powerful because once you know k, you can find any y for any x, and vice versa. To find k, simply divide: k = y ÷ x. Try it with multiple pairs in a table to confirm the relationship is truly proportional before trusting your answer.
| Hours Worked (x) | Money Earned (y) | y ÷ x | Proportional? |
|---|---|---|---|
| 1 | $12 | 12 | Yes |
| 2 | $24 | 12 | Yes |
| 3 | $36 | 12 | Yes |
| 4 | $50 | 12.5 | No — ratio changed! |
| Feature | Proportional | Not Proportional |
|---|---|---|
| Line type | Straight line | Curved or straight |
| Passes through (0,0) | Always yes | Not necessarily |
| Constant ratio y/x | Always the same | Changes |
Key terms
- Proportional relationship
- A relationship between two quantities where their ratio is always the same
- Constant of proportionality (k)
- The fixed ratio between y and x in a proportional relationship; the value in y = kx
- Unit rate
- The ratio when the denominator is 1, such as $3 per 1 pound
- Origin
- The point (0, 0) on a graph; proportional relationships always pass through it
- Ratio
- A comparison of two quantities using division
Practice questions
A car travels 150 miles in 3 hours at a constant speed. Which equation models this proportional relationship where y = miles and x = hours?
- y = 3x
- y = 50x
- y = 150x
- y = 0.02x
Show answer
Answer: y = 50x
A graph that represents a proportional relationship must be a straight line passing through the origin.
Show answer
Answer: True
In the equation y = kx, the value of k is called the constant of ___.
Show answer
Answer: proportionality
A table shows: x = 2, y = 8; x = 4, y = 16; x = 6, y = 25. Is this a proportional relationship?
- Yes, because the values increase
- No, because the ratio y/x is not constant
- Yes, because the graph is a straight line
- No, because x and y are different numbers
Show answer
Answer: No, because the ratio y/x is not constant
If 4 gallons of paint cover 200 square feet, then 10 gallons will cover 500 square feet, assuming a proportional relationship.
Show answer
Answer: True
Fun facts
- The ancient Egyptians used proportional reasoning to build the pyramids — scaling up blueprints using the same ratios they sketched on small papyrus scrolls.
- GPS navigation apps use proportional relationships every time they convert real-world distances to pixels on your screen at different zoom levels.
Get a personalized course on Proportional Relationships built around your child.