Graphs showing inverse proportion | Maths | Quizalize & Oak National Academy

Starter quiz

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 ...

be in direct proportion to each other. ✓

be unrelated.

have a changing rate of change.
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?

It takes 5 hours to walk 20 km.

It takes 20 hours to walk 5 km.

It takes 5 hours to walk 20 miles. ✓

It takes 20 hours to walk 5 miles.
What is the equation of the line in this distance-time graph? Use $d$ for distance travelled and $t$ for time taken.

$d=5t$

$t=5d$

$d=4t$ ✓

$4d=t$

$d=t+4$
For the equation $s={30\over{t}}$ , when $t=7.5$ , $s=$ ______.

'4' ✓
For the equation $s={30\over{t}}$ , when $s=7.5$ , $t=$ ______

'4' ✓

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

increases.

decreases. ✓

remains constant.
Inversely proportional relationships are modelled by the relationship ...

$ky=x$

$y=kx$

$y={x\over{k}}$

$y={k\over{x}}$ ✓
Which of these graphs shows a relationship of indirect proportion?
Why can this not be a graph of indirect proportion?

Indirect proportion graphs do not intersect either axis. ✓

It is not a straight line.

It is decreasing as the horizontal variable decreases.

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

3

5

5 people

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

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

'10' ✓

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Solutions for context-based problem can be listed as coordinate pairs with units e.g. 6 workers, 60 hours.

Solutions should always be fully interpreted in relation to the context e.g. It would take 6 workers 60 hours to paint the building.

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