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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

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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Share activities with pupils

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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.

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?

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

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

$$375\div375\times30$$