Checking and securing understanding of finding the equation of the line from the graph | Maths

Starter quiz

What is the step on the $y$ axis of this graph?

0.5

1

2 ✓

10
A jug of drink is made from 6 cups of juice and 18 cups of soda. Use the ratio table to work out the amount of soda needed for 1 cup of juice.

'3' ✓
What is the missing value in this ratio table?

0.6

$2\over 3$ ✓

1

$3\over 2$

6
A table of values is shown for the relationship $y = 12 - 4x$ . Which of these is true for this relationship?

For every change of +1 in $x$ there is a change of -4 in $y$ ✓

For every change of +1 in $x$ there is a change of +4 in $y$

For every change of +1 in $y$ there is a change of -4 in $x$

For every change of +5 in $x$ there is a change of -20 in $y$ ✓

For every change of +12 in $y$ there is a change of +3 in $x$
Match each keyword to its definition.

constant

⇔

a term that does not vary ✓

coefficient

⇔

the multiplier of a specified variable in a term ✓

gradient

⇔

a measure of how steep a line is ✓

intercept

⇔

the point where a line crosses a specified axis ✓

origin

⇔

the point with coordinates (0, 0) ✓

equation of a straight line

⇔

a relationship which, when plotted, forms a straight line ✓
Match each equation of a line to its key features.

$y = 3x − 2$

⇔

gradient 3, $y$ -intercept (0, -2) ✓

$y = 3x + 2$

⇔

gradient 3, $y$ -intercept (0, 2) ✓

$y = 2 - 3x$

⇔

gradient -3, $y$ -intercept (0, 2) ✓

$y = 2x - 3$

⇔

gradient 2, $y$ -intercept (0, -3) ✓

$y = 3 + 2x$

⇔

gradient 2, $y$ -intercept (0, 3) ✓

$y = 3 - 2x$

⇔

gradient -2, $y$ -intercept (0, 3) ✓

Exit quiz

Which of these descriptions best describes the gradient?

How much the $x$ values change for every 1 increase in $y$

How much the $y$ values change for every 1 increase in $x$ ✓

How much the $x$ values change for every 1 decrease in $y$

How much the $y$ values change for every 1 decrease in $x$
The gradient of this line is ______.

'3' ✓
The gradient of this line is ______.

'-2' ✓
The gradient of this line is ______.

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

$y=-{1\over 3}x - 2$

$y=-{1\over 3}x + 2$

$y={1\over 3}x - 2$ ✓

$y=3x - 2$

$y=2 - 3x$
Match each line to its correct equation.

A (blue)

⇔

$y=-{2\over 3}x - 2$ ✓

B (pink)

⇔

$y=-{3\over 2}x - 2$ ✓

C (black)

⇔

$y={3\over 2}x$ ✓

D (green)

⇔

$y={3\over 2}x - 2$ ✓

E (purple)

⇔

$y={2\over 3}x - 2$ ✓

Worksheet

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Lesson Details

Key learning points

Linear equations can be rearranged into the form y = mx + c
The gradient (m) and the y-intercept (c) can be determined from the graph.
The amount y changes when x increases by one is the rate of change and called the gradient.
Where the graph crosses the y-axis is the value of the y-intercept.
The equation of the line can be written in the form y = mx + c

Common misconception

Writing equations of the form y = mx + c and getting the gradient and y-intercept the wrong way round.

Graphing software can be used to show that adding a constant is a translation of the graph. Remind pupils that the y-intercept is when x is zero which is why it is the constant in the equation. They can substitute x = 0 to check.

Keywords

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 coordinate where a line or curve meets a given axis.