Identifying Proportional Relationships by Graphing

Let’s Explore the World of Proportions! 

Have you ever wondered why doubling a recipe keeps the taste the same? Or why the speed of a car and the time it takes to travel are connected? These are examples of proportional relationships, and one of the best ways to identify them is by using graphs!

A proportional relationship means that two quantities change at a constant rate. When you graph this relationship, something special happens—it always forms a straight line that passes through the origin (0,0).

How to Identify Proportional Relationships on a Graph

Step 1: Create a Table of Values

Start with a real-world situation and create a table comparing two related quantities (like distance and time, price and weight, etc.).

Step 2: Plot the Points on a Graph

Take the values from your table and place them on a coordinate plane.

Step 3: Check the Line

A proportional relationship will always:

Form a straight line

Pass through the origin (0,0)

If the line curves or doesn’t go through the origin, the relationship is not proportional.

Solved Example: Is This a Proportional Relationship?

Emma works as a dog walker. She charges a fixed amount per hour. The table below shows her earnings:

Hours           Worked Money Earned ($)

1                                          15

2                                         30

3                                         45

4                                         60

Step 1: Plot the Points

We graph the points:

(1,15), (2,30), (3,45), (4,60)

Step 2: Check the Pattern

The points form a straight line

The line passes through the origin (0,0)

Since both conditions are met, this is a proportional relationship!

Fun Facts About Proportional Graphs!

If a graph represents a proportional relationship, the equation will always be in the form y = kx, where k is the constant of proportionality.

If a graph is not a straight line or doesn’t go through (0,0), the relationship is not proportional.

Proportional graphs appear in speed vs. time, price vs. weight, distance vs. time, and so much more!

Real-Life Applications:

Proportions are everywhere! Whether you’re doubling a recipe, calculating the time it takes for a road trip, converting currencies, or figuring out how long it’ll take to binge-watch your favorite show, you’re using proportions. Knowing how to spot and solve them makes life so much easier.

Let's explore proportions through graphs helps make sense of the world around us!