Graphs of Proportion
Maths: Edexcel A Level Pure Maths, topic 2.5.4
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.
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.
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.
Test yourself on Graphs of Proportion
In a straight line graph with the equation 'y = 4x - 2', is y directly proportional to x?
In a straight line graph with the equation 'y = 3x', is y directly proportional to x?
Which letter represents the slope of a straight line graph of two variables that are directly proportional?
What is the equation for this straight line graph?
What is the unit rate of the graph shown?