Two variables are in direct proportion if they have a constant multiplicative relationship.

Checking and understanding graphs showing direct proportion

Maths

The work on gradient in this unit is expanded further in the future unit by considering gradient as the rate of change and interpreting this in context. The gradient of the tangent is introduced as a way of estimating the gradient of a curve.

In the prior unit, pupils drew a linear graph from its equation and related the features of the graph to its equation. In this unit, pupils consider equations that produce parallel or perpendicular graphs and how their equations relate to each other.

Linear graphs

Graphs of direct proportion intersect the axes at the {{}}.

Graphs of direct proportion begin at the origin and ...

Select the graphs that represent direct proportion.

For the coordinates (8, 20) and (10, 25), $$x$$ and $$y$$ are in direct proportion. Which of these coordinates also represent this same direct proportion?

The point P lies on this direct proportion graph. The $$y$$-coordinate of P is $$25$$, the $$x$$-coordinate of P is {{ }}.

The point P lies on this direct proportion graph. The $$x$$-coordinate of P is $$375$$. Which of these calculations can you use to find the $$y$$-coordinate of P?

If two variables share a constant multiplicative relationship they are in direct {{}} to one another.

There is no constant multiplicative relationship.

$$x$$ and $$y$$ are never in direct proportion.

The table shows that they are in direct proportion.

In this example how can you tell that the variables $$x$$ and $$y$$ are not in direct proportion?

The cost of hiring headphones at a festival is directly proportional to the time you hire them for. If two hours cost £16, how much should five hours cost?

The gradient of a straight line that passes through coordinates (10, 18) and (17, 53) is {{}}

Find the equation of the straight line that goes through coordinates (8, -1) and  (12, 1).

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Checking and understanding graphs showing direct proportion

Lesson outcome