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Year 10
Higher

Checking and understanding graphs showing direct proportion

I can recognise direct proportion graphically and can interpret graphs that illustrate direct proportion.

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New
New
Year 10
Higher

Checking and understanding graphs showing direct proportion

I can recognise direct proportion graphically and can interpret graphs that illustrate direct proportion.

Download all resources
Share activities with pupils

Lesson details

Key learning points

  1. Direct proportion can be recognised graphically.
  2. The equation of a direct proportion graph is of the form y = kx
  3. The origin is always a point on a direct proportion graph.
  4. The gradient tells us the constant of proportionality.

Common misconception

Direct proportion can be determined by calculating the gradient.

The equation of the line should be of the form y = kx and so the y-intercept should be calculated to check it is zero.

Keywords

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

k is used as the notation for the gradient here for two reasons. It is to show that other letters can represent gradient and to prepare for the Year 11 unit where k is formally referred to as the constant of proportionality.
Teacher tip

Licence

This content is © Oak National Academy Limited (2024), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

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Starter quiz

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6 Questions

Q1.
If two variables share a constant multiplicative relationship they are in direct to one another.
Correct Answer: proportion
Q2.
In this example how can you tell that the variables $$x$$ and $$y$$ are not in direct proportion?
An image in a quiz
The multiplications are wrong.
Correct answer: There is no constant multiplicative relationship.
$$x$$ and $$y$$ are never in direct proportion.
The table shows that they are in direct proportion.
Q3.
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?
£8
£32
Correct answer: £40
£80
£128
Q4.
The gradient of a straight line that passes through coordinates (10, 18) and (17, 53) is
Correct Answer: 5, Five, five
Q5.
What is the equation of this line?
An image in a quiz
$$y=x+3$$
$$x+y=3$$
$$3y=x$$
Correct answer: $$y=3x$$
$$y=3x+3$$
Q6.
Find the equation of the straight line that goes through coordinates (8, -1) and (12, 1).
$$y=2x-15$$
$$y=2x-23$$
$$y=3-{1\over2}x$$
$$y=7-{1\over2}x$$
Correct answer: $$y={1\over2}x-5$$

Exit quiz

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6 Questions

Q1.
Graphs of direct proportion intersect the axes at the .
Correct Answer: origin, Origin
Q2.
Graphs of direct proportion begin at the origin and ...
are curved.
Correct answer: have a constant gradient.
have a changing gradient.
Correct answer: have a constant rate of change.
Q3.
Select the graphs that represent direct proportion.
Correct Answer: An image in a quiz
An image in a quiz
An image in a quiz
An image in a quiz
Correct Answer: An image in a quiz
An image in a quiz
Q4.
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?
(9, 21)
Correct answer: (12, 30)
(15, 30)
Correct answer: (24, 60)
Correct answer: (1, 2.5)
Q5.
The point P lies on this direct proportion graph. The $$y$$-coordinate of P is $$25$$, the $$x$$-coordinate of P is .
An image in a quiz
Correct Answer: 2, x=2, x = 2, two
Q6.
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?
An image in a quiz
Correct answer: $$375\times12.5$$
$$375\div12.5$$
Correct answer: $$375\times375\div30$$
Correct answer: $${375\over30}\times375$$
$$375\div375\times30$$