2.5.4

Graphs of Proportion

Test yourself

Direct and Inverse Proportion Graphs

We can show the two different types of proportionality between two variables on a graph.

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Direct proportion

  • If y and x are directly proportional, the graph of the relationship will be a straight line graph.
  • It must pass through the origin.
  • It could have a negative slope.
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y = 2x

  • For every increase in x, y increases by twice that amount.
  • Since it goes through the origin, y is always double x.
  • y is directly proportional to x with k = 2.
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y = 2x + 3

  • This graph shows y = 2x + 3.
  • Every increase in x corresponds to twice that increase in y.
  • y is not directly proportional to x because of the '+ 3'.
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Inverse proportion

  • If y and x are inversely proportional then the graph is a curved line that never touches the x or y axes.
  • Part of the graph lies in quadrant I and part of the graph lies in quadrant III.
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Unit rate

  • The constant of proportionality can also be thought of as a unit rate, or "y per unit x".
  • The unit rate is equal to the y-coordinate of the graph when x = 1.

Jump to other topics

1Proof

2Algebra & Functions

2.1Powers & Roots

2.2Quadratic Equations

2.3Inequalities

2.4Polynomials

2.5Graphs

2.6Functions

2.7Transformation of Graphs

2.8Partial Fractions (A2 Only)

3Coordinate Geometry

4Sequences & Series

5Trigonometry

6Exponentials & Logarithms

7Differentiation

8Integration

9Numerical Methods

10Vectors

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