Identify Proportional Relationships from Equations

Standard: 7.RP.A.2a

Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin.

Learning Outcomes

After completing this worksheet, students will be able to:
Recognize proportional relationships in algebraic equations
Understand the key structure of proportional equations: y = kx
Graph linear equations and interpret their visual meaning
Explain whether a relationship is proportional using both algebraic and graphical reasoning
Build connections between real-world situations and math models

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Grade Level: 7
Standard: 7.RP.A.2a – Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin.

Topic Overview: What Is a Proportional Relationship?

A proportional relationship is one where two quantities grow or shrink at the same constant rate. When graphed, this relationship creates a straight line that passes through the origin (0,0). In math terms, this is shown by the equation y = kx, where:

y is the dependent variable
x is the independent variable
k is the constant of proportionality (also called the unit rate)

This worksheet helps 7th-grade students understand how to analyze equations and their graphs to determine whether a relationship is proportional.

Real-World Background Scenario

Imagine you're running a lemonade stand. You charge $2 per glass. So if you sell 1 glass, you earn $2. Sell 2 glasses, earn $4. This is a proportional relationship — your income grows at a constant rate of $2 per glass. Graph it, and the line passes right through the origin. That's exactly what we look for when deciding if equations are proportional!

Solved Example:

Question: Is the equation y = 4x proportional?

Let’s analyze it step by step:

Step 1: Check the equation form

The equation y = 4x is in the form y = kx, where k = 4.

So far, so good!

Step 2: Graph the equation

Choose x-values: 0, 1, 2, 3
Now calculate y-values:

x	y = 4x
0	0
1	4
2	8
3	12

Plot the points (0,0), (1,4), (2,8), (3,12). You’ll see the line:

Goes through the origin and forms a straight line.

Conclusion:

Yes, y = 4x is proportional because:

It's in the form y = kx
The graph is a straight line through the origin

Try It Yourself – Questions on the Worksheet

Is y = 11x proportional?
- Graph the equation and analyze: Is it in the form y = kx?
- Does it pass through (0,0)?
- (Spoiler: Yes, it’s proportional.)
Is y = 5 + 3x proportional?
- Uh-oh! This one includes a constant (5).
- Even though it forms a line, it doesn’t pass through the origin.
- So, it's not proportional.

This worksheet is ideal for reinforcing graphing skills and deepening student's understanding of ratios, equations, and proportionality all while connecting algebra to real-world situations.