Checking and understanding graphs showing direct proportion | Maths

Starter quiz

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

'proportion' ✓
In this example how can you tell that the variables $x$ and $y$ are not in direct proportion?

The multiplications are wrong.

There is no constant multiplicative relationship. ✓

$x$ and $y$ are never in direct proportion.

The table shows that they are in direct proportion.
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

£40 ✓

£80

£128
The gradient of a straight line that passes through coordinates (10, 18) and (17, 53) is ______

'5' ✓
What is the equation of this line?

$y=x+3$

$x+y=3$

$3y=x$

$y=3x$ ✓

$y=3x+3$
Find the equation of the straight line that goes through coordinates (8, -1) and (12, 1).

$y=2x-15$

$y=2x-23$

$y=3-{1\over2}x$

$y=7-{1\over2}x$

$y={1\over2}x-5$ ✓

Graphs of direct proportion intersect the axes at the ______.

'origin' ✓
Graphs of direct proportion begin at the origin and ...

are curved.

have a constant gradient. ✓

have a changing gradient.

have a constant rate of change. ✓
Select the graphs that represent direct proportion.
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)

(12, 30) ✓

(15, 30)

(24, 60) ✓

(1, 2.5) ✓
The point P lies on this direct proportion graph. The $y$ -coordinate of P is $25$ , the $x$ -coordinate of P is ______.

'2' ✓
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?

$375\times12.5$ ✓

$375\div12.5$

$375\times375\div30$ ✓

${375\over30}\times375$ ✓

$375\div375\times30$

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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.

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