Graphs & Proportion
Maths: Edexcel IGCSE Higher, topic 2.5.1
Gradient of a Straight Line Graph
For a straight line graph the gradient is the constant of proportionality k. y = kx.
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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'.
Direct and Inverse Proportions as Graphs
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 gradient.
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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 the top right quadrant and part of the graph lies in the bottom left quadrant.
Test yourself on Graphs & 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 gradient of a straight line graph?
What is the equation for this straight line graph?
What is the equation for the gradient of a line?