Calculating the rate of change | Maths | Quizalize & Oak National Academy

Starter quiz

In this table there is a __________ rate of change in the $y$ values.

constant ✓

negative

increasing

decreasing
In this table for every change of $+1$ in $x$ there is a change of _________ in $y$ .

$-8$

$-6$

$+4$

$+6$ ✓

$+10$
How do we know there is not a constant rate of change between the $x$ and $y$ variables in this graph?

The graph is not decreasing.

It is not a linear graph. ✓

The graph has a positive gradient.

The graph does not intercept the $y$ -axis at the origin.
What is the gradient of this line?

$+2$

$+4$

$-3$ ✓

$-6$
When we find the gradient on a distance-time graph we have calculated the __________ of the particle being modelled.

distance travelled

displacement

speed ✓

acceleration

deceleration
What is the gradient of this line?

$3$

$3\over2$ ✓

$2\over3$

$-{3\over2}$

$-2$

Exit quiz

What is the gradient of this line?

$+10$

$+2$

$-10$

$-5$ ✓
What is the gradient of this line?

$1$

$2$

$4$

$8$ ✓

$0.25$
$This is a conversion graph for British Pounds (<Math>\pounds</Math>) to New Zealand Dollars (<Math>{\$}</Math>) and the gradient of the line is <Math>2</Math>. Which of the below statements are accurate?$

This is a conversion graph for British Pounds ( $\pounds$ ) to New Zealand Dollars ( ${\$}$ ) and the gradient of the line is $2$ . Which of the below statements are accurate?

Every one New Zealand Dollar is worth two British Pounds.

Every one British Pound is worth two New Zealand Dollars. ✓

For every change of $+1$ in $\pounds$ there is a change of $+2$ in ${\$}$ ✓

For every change of $+1$ in ${\$}$ there is a change of $+2$ in $\pounds$

For every change of $+10$ in ${\$}$ there is a change of $+20$ in $\pounds$
What is the speed of the vehicle modelled in this distance-time graph?

$2$ km/h

$60$ km/h ✓

$120$ km/h

$240$ km/h
$This graph shows the charges of a taxi firm in <Math>\pounds</Math> for every mile (<Math>m</Math>) travelled. Which of these statements are accurate about the rate of change for this taxi firm's charges?$

This graph shows the charges of a taxi firm in $\pounds$ for every mile ( $m$ ) travelled. Which of these statements are accurate about the rate of change for this taxi firm's charges?

Cost changes by $\pounds2$

The rate of change of the cost is $\pounds2$ per mile. ✓

Journeys cost $\pounds2$ per mile.

Every extra mile travelled adds $\pounds2$ to the cost. ✓
How much faster is this vehicle travelling in the first hour of its journey versus the sixth hour?

$60$ km/h

$50$ km/h ✓

$40$ km/h

$10$ km/h

$110$ km/h

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Lesson Details

Key learning points

For straight-line sections of a graph, it is easy to calculate the gradient.
The gradient tells us the rate that one quantity changes with respect to the other.
The gradient gives the rate that the $y$ variable changes with respect to the $x$ variable.
The gradient can be interpreted in context and should be for real life contexts.

Common misconception

Gradient is change in $y$ divided by change in $x$ .

The gradient is calculated by considering the change in $y$ when moving one unit in the positive $x$ direction.

Keywords

Rate of change - The rate of change is how one variable changes with respect to another. If the change is constant, there is a linear relationship between the variables.
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.