Two variables are inversely proportional if there is a constant multiplicative relationship between one variable and the reciprocal of the other.

Graphs showing inverse 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

When two variables are indirectly proportional, as one variable increases the other ...

Inversely proportional relationships are modelled by the relationship ...

Which of these graphs shows a relationship of indirect proportion?

Indirect proportion graphs do not intersect either axis.

It is decreasing as the horizontal variable decreases.

Indirect graphs have the form $$y={k\over{x}}$$ , dividing by zero is undefined.

Why can this not be a graph of indirect proportion?

It would take 3 people 5 days to dig the hole.

It would take 5 people 3 days to dig the hole.

This graph plots the time taken ($$t$$) in days for a varying number of people ($$p$$) to dig a hole. How long would it take 3 people?

This graph shows the relationship between people and time required to build a wall. The point marked shows that 10 people would take 3 days. It would take 3 people {{}} days to build the wall.

If it takes 2 hours to walk 6 miles, 3 hours to walk 9 miles, and 4 hours to walk 12 miles then the variables time and distance are said to ...

Which of these graphs shows a directly proportional relationship?

This time distance graph shows the relationship between the hours walked and the distance travelled in miles. What do the coordinates (5, 20) show?

What is the equation of the line in this distance-time graph? Use $$d$$ for distance travelled and $$t$$ for time taken.

For the equation $$s={30\over{t}}$$, when $$t=7.5$$, $$s=$${{}}.

For the equation $$s={30\over{t}}$$, when $$s=7.5$$, $$t=$${{}}

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