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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

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

Direct proportion can be recognised graphically.
The equation of a direct proportion graph is of the form y = kx
The origin is always a point on a direct proportion graph.
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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This content is © Oak National Academy Limited (2025), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

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Prior knowledge 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?

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?

$$y=x+3$$

$$x+y=3$$

$$3y=x$$

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: $$y={1\over2}x-5$$

Assessment 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

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 .

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?

Correct answer: $$375\times12.5$$

$$375\div12.5$$

Correct answer: $$375\times375\div30$$

Correct answer: $${375\over30}\times375$$

$$375\div375\times30$$

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UnitMaths / Linear graphs

Maths

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Checking and understanding graphs showing direct proportion

Checking and understanding graphs showing direct proportion

Lesson slides

Lesson details

Key learning points

Keywords

Common misconception

Licence

Lesson video

Worksheet

Prior knowledge starter quiz

6 Questions

Q1.If two variables share a constant multiplicative relationship they are in direct to one another.

Q2.In this example how can you tell that the variables $$x$$ and $$y$$ are not 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?

Q4.The gradient of a straight line that passes through coordinates (10, 18) and (17, 53) is

Q5.What is the equation of this line?

Q6.Find the equation of the straight line that goes through coordinates (8, -1) and (12, 1).

Assessment exit quiz

6 Questions

Q1.Graphs of direct proportion intersect the axes at the .

Q2.Graphs of direct proportion begin at the origin and ...

Q3.Select the graphs that represent direct proportion.

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?

Q5.The point P lies on this direct proportion graph. The $$y$$-coordinate of P is $$25$$, the $$x$$-coordinate of P is .

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?

Lesson appears in

UnitMaths / Linear graphs

Maths

Q1.
If two variables share a constant multiplicative relationship they are in direct to one another.

Q2.
In this example how can you tell that the variables $$x$$ and $$y$$ are not 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?

Q4.
The gradient of a straight line that passes through coordinates (10, 18) and (17, 53) is

Q5.
What is the equation of this line?

Q6.
Find the equation of the straight line that goes through coordinates (8, -1) and (12, 1).

Q1.
Graphs of direct proportion intersect the axes at the .

Q2.
Graphs of direct proportion begin at the origin and ...

Q3.
Select the graphs that represent direct proportion.

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?

Q5.
The point P lies on this direct proportion graph. The $$y$$-coordinate of P is $$25$$, the $$x$$-coordinate of P is .

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?