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Checking and securing understanding of direct proportion graphs

I can identify direct proportion graphs from their features and can use the graph to create an equation to algebraically model this relationship.

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Year 11

Checking and securing understanding of direct proportion graphs

I can identify direct proportion graphs from their features and can use the graph to create an equation to algebraically model this relationship.

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Key learning points

Direct proportion can be recognised graphically.
A direct proportion graph is always a straight line through the origin.
The gradient is the constant of proportionality.
The equation of the line can be found and this is the algebraic model of the relationship.

Keywords

Direct proportion - Two variables are in direct proportion if they have a constant multiplicative relationship
Gradient - The gradient is a measure of how steep a line is. It is calculated by finding the rate of change in the y-direction with respect to the positive x-direction
Intercept - An intercept is the point where a line or curve meets a given axis

Common misconception

Assuming that any linear graph with a constant positive gradient shows a directly proportional relationship.

Using examples in a context really helps here. E.g. 'I change £0. How many dollars do I get?, I travel 0 miles. How many kilometres have I travelled?

The language used in the second learning cycle is important. The fact that the coefficient of x, rate of change of y as x increases, the gradient and constant or proportionality are effectively the same thing. Give pupils time to practice using the different phrases.

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