Checking and securing understanding of direct proportion graphs | Maths

Starter quiz

The ______ is the measure of how steep a line is.

'gradient' ✓
Match each to the missing number that would replace the question mark.

18 × ? = 72

⇔

4 ✓

16 × ? = 4

⇔

$1\over4$ ✓

36 × ? = 27

⇔

$3\over4$ ✓

? × 27 = 36

⇔

$4\over3$ ✓

? × 16.2 = 48.6

⇔

3 ✓

2.4 × ? = 0.8

⇔

$1\over3$ ✓
The cost of 3 apples is £1.59. What is the cost of 36 apples?

'£19.08' ✓
The exchange rate is £1 : €1.18. How many Euros would you get if you exchanged £300?

'354' ✓
Using the exchange rate £1 : $1.27. Which of the following are true?

£560 = $710.20

£100 = $127 ✓

£860 = $1092.20 ✓

£18 = $22.80

£475 = $603.25 ✓
A recipe says that you need 330 g of butter to make 30 cookies. How much butter do you need to make 255 cookies?

'2805 g' ✓

If two variables have a constant multiplicative relationship, they are in ______ proportion.

'direct' ✓
Which of the following tables show values of A and B in direct proportion?
Which of the following graphs show direct proportion?
Calculate the value of k (constant of proportionality).

$3\over4$ ✓

1.5

$4\over3$

$5\over4$
What is the equation of this line?

$y={4\over3}x$

$y={3\over4}$

$y={4\over3}$

$y={3\over4}x$ ✓
Which is the graph of $y={5\over4}x$ ?

A

B

C ✓

D

Loading worksheet ...

Loading presentation ...

Direct proportion can be recognised graphically.
A direct proportion graph is always a straight line through the origin.
The gradient is the constant of proportionality.
The equation of the line can be found and this is the algebraic model of the relationship.

Assuming that any linear graph with a constant positive gradient shows a directly proportional relationship.

Using examples in a context really helps here. E.g. 'I change £0. How many dollars do I get?, I travel 0 miles. How many kilometres have I travelled?

Direct proportion - Two variables are in direct proportion if they have a constant multiplicative relationship
Gradient - The gradient is a measure of how steep a line is. It is calculated by finding the rate of change in the y-direction with respect to the positive x-direction
Intercept - An intercept is the point where a line or curve meets a given axis