Pre-Algebra
Proportional relationships
Proportional relationships
20 practice questions
0 video lessons
Theory + worked examples
Proportional Relationships
Common Core Pre-Algebra • Standard 7.RP.2 • Proportional Relationships
Proportional Relationships is the opening topic of Proportional Relationships in the Common Core State Standards. It is aligned to Standard 7.RP.2, which requires students to recognize and represent proportional relationships.
A proportional relationship has a constant ratio between the quantities and graphs as a straight line through the origin.
Theory
Two quantities are in a proportional relationship when their ratio is constant: \(y=kx\).
The graph is a straight line through the origin \((0,0)\).
A line through the origin.
What makes a relationship proportional.
The form:
\[y=kx,\qquad \dfrac{y}{x}=k\]
Passing through the origin is the key test.
How to test for proportionality
- Check the ratio \(\dfrac{y}{x}\) is constant.
- Check the graph passes through the origin.
- If both hold, it is proportional.
- The constant ratio is \(k\).
Example 1 — Test it
Is \(y=2x\) proportional?
Solution
Yes — line through the origin, constant ratio \(2\).
Example 2 — Not proportional
Is \(y=2x+3\) proportional?
Solution
No — it does not pass through the origin.
Example 3 — From a table
A table has \((2,6)\) and \((4,12)\). Proportional?
Solution
Both give \(\dfrac{y}{x}=3\), so yes.
| \(\dfrac{6}{2}=\dfrac{12}{4}\) | \(=\) | \(3\) |
Example 4 — Find y
If \(y\) is proportional to \(x\) with \(k=5\), find \(y\) at \(x=4\).
Solution
Use \(y=kx\).
| \(y\) | \(=\) | \(5\cdot4=20\) |
Common pitfalls
\(y=mx+b\) with \(b\neq0\) is not proportional.
The ratio must be constant for every pair.
It must pass through the origin.
Frequently asked questions
What is a proportional relationship?
One with a constant ratio, \(y=kx\).
How can I tell from a graph?
It is a straight line through the origin.
Is \(y=2x+3\) proportional?
No.
What is k?
The constant ratio \(y/x\).
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