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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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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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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.

Keywords

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

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.

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.
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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).

Lesson video

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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: $${375\over30}\times375$$
$$375\div375\times30$$