This engaging worksheet helps students dive into one of the most important concepts in proportional relationships — the constant of proportionality (k). By using graphs and coordinate points, learners will practice finding the value of k, which tells us how two values are related in a consistent, proportional way.

Perfect for visual learners, this activity builds a strong foundation for working with equations like y = kx and understanding proportional patterns in real life.

What You'll Learn:

• How to read coordinate points from a graph.

• How to calculate the constant of proportionality (k).

• How to use the formula k = y / x (when y and x come from a proportional pair).

• How to apply the concept of unit rate in a real graph-based setting.

Solved Example (From Question 1 on Sheet)

Question:
From the graph of points (1, 10), (2, 20), (3, 30), find the constant of proportionality.

Step-by-Step Solution:

1. Choose any point from the graph, e.g., (2, 20).

2. Use the formula:
   k = y / x = 20 / 2 = 10

3. Check other points to confirm:

   • (1, 10) → 10 / 1 = 10

   • (3, 30) → 30 / 3 = 10

So, the constant of proportionality (k) = 10

Try These on Your Own:

• Q2: Use points like (3, 9), (4, 12) from the graph. Apply the same method: k = y / x

• Q3 & Q4: No graph given? No worries! The points are listed, so students must plot them or just plug into the formula.

Did You Know?

• The constant k is the same as the unit rate.

• If you multiply x by k, you’ll always get y in a proportional relationship.

• This is how many real-world problems — like price per item or speed — are solved using math!

 Great For:

• Grade 7 ratio & proportion units

• Visual learners who enjoy graphs

• Strengthening skills before algebra

• Homework, classwork, or math centers

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