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?

  1. A car can travel 200 km with 12 L of fuel and other 300 km with 20 L of fuel.
  2. 5 kg of paint can paint 30 m2 wall while 12 kg paint can paint 72 m2 wall.

Solution 3

  1. 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.
  2. 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 IDMath Tutorial TitleTutorialVideo
Lesson IDMath Lesson TitleLessonVideo
4.3.1Definition of Proportion
4.3.2Direct Proportion
4.3.3Graph of Direct Proportion
4.3.4Cross Product in Direct Proportion
4.3.5Inverse (Indirect) Proportion
4.3.6Graph of Inverse Proportion

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  3. 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
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  5. Ratio and Proportion Practice Questions: Proportion. Test and improve your knowledge of Proportion with example questins and answers
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  7. Continuing learning ratio and proportion - read our next math tutorial: Properties of Proportion. Geometric Mean

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