Math Lesson 4.3.3 - Graph of Direct Proportion

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Welcome to our Math lesson on Graph of Direct Proportion, this is the third lesson of our suite of math lessons covering the topic of Proportion, you can find links to the other lessons within this tutorial and access additional Math learning resources below this lesson.

Graph of Direct Proportion

In ratio tutorial 4.1 we proved that ratios produce a linear graph. Since the direct proportion is obtained by two equal ratios, it is easy to conclude that the graph representing a direct proportion is a straight (sloped) line that starts from the origin (otherwise it is not a direct proportion), where the slope is determined by the simplest form of the ratio or of the unit rate.

Let's consider one such a graph to clarify this point.

The graph below is not an example of direct proportion because the ratios of position at the two given instants are not the same as the ratios of time. In other words, 320/110 is different from 20/10, as the first ratio gives 1.5 and the second gives 2. $Math Tutorials: Proportion Example$

Therefore, the quantities involved in the above situation are not directly proportional. In simpler words, the graph must start from the origin in order to have a direct proportion, as shown below.

$Math Tutorials: Proportion Example$

Here, both ratios are the same as 220/110= 20/10 = 2. Therefore, the quantities involved are directly proportional (or simply, proportional).

Remark! It is better to solve the situations with ratios, not with rates when dealing with proportions. In other words, it is better to divide two like quantities instead of the unlike ones.

Example 3

Which of the following situations involves a direct proportion?

A car can travel 200 km with 12 L of fuel and other 300 km with 20 L of fuel.
5 kg of paint can paint 30 m² wall while 12 kg paint can paint 72 m² wall.

Solution 3

We will check whether the ratios are equal by dividing the like quantities. We have
200 km distance/300 km distance and 12 L fuel/20 L fuel
The first fraction gives 2/3 while the second gives 3/5. Therefore, this situation does not involve a direct proportion.
Again, we take the ratios. We have
5 kg paint/12 kg paint and 30 m² wall/72 m² wall
The first ratio is already in the simplest form, and the second ratio gives 5/12 too when written in the simplest terms. Therefore, the quantities involved are proportional.

More Proportion Lessons and Learning Resources

Ratio and Proportion Learning Material
Tutorial ID	Math Tutorial Title	Revision Notes	Revision Questions
4.3	Proportion
Lesson ID	Math Lesson Title	Lesson	Video Lesson
4.3.1	Definition of Proportion
4.3.2	Direct Proportion
4.3.3	Graph of Direct Proportion
4.3.4	Cross Product in Direct Proportion
4.3.5	Inverse (Indirect) Proportion
4.3.6	Graph of Inverse Proportion

Whats next?

Enjoy the "Graph of Direct Proportion" math lesson? People who liked the "Proportion lesson found the following resources useful:

Graph Feedback. Helps other - Leave a rating for this graph (see below)
Ratio and Proportion Math tutorial: Proportion. Read the Proportion math tutorial and build your math knowledge of Ratio and Proportion
Ratio and Proportion Video tutorial: Proportion. Watch or listen to the Proportion video tutorial, a useful way to help you revise when travelling to and from school/college
Ratio and Proportion Revision Notes: Proportion. Print the notes so you can revise the key points covered in the math tutorial for Proportion
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Check your calculations for Ratio and Proportion questions with our excellent Ratio and Proportion calculators which contain full equations and calculations clearly displayed line by line. See the Ratio and Proportion Calculators by iCalculator™ below.
Continuing learning ratio and proportion - read our next math tutorial: Properties of Proportion. Geometric Mean

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