New
New
Year 10
Foundation

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

I can find the equation of the line from the graph.

New
New
Year 10
Foundation

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

I can find the equation of the line from the graph.

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Lesson details

Key learning points

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

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.

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.

This builds on KS3 work where pupils found equations by looking at the relationship between x and y values within a coordinate pair. Remind them that any coordinate pair on the line should satisfy their equation. They can use this to check their equations seem reasonable.
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).

Lesson video

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6 Questions

Q1.
What is the step on the $$y$$ axis of this graph?
An image in a quiz
0.5
1
Correct answer: 2
10
Q2.
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.
An image in a quiz
Correct Answer: 3, 3 cups, three, three cups
Q3.
What is the missing value in this ratio table?
An image in a quiz
0.6
Correct answer: $$2\over 3$$
1
$$3\over 2$$
6
Q4.
A table of values is shown for the relationship $$y = 12 - 4x$$. Which of these is true for this relationship?
An image in a quiz
Correct answer: 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 $$x$$
Correct answer: 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 $$x$$
Q5.
Match each keyword to its definition.
Correct Answer:constant ,a term that does not vary

a term that does not vary

Correct Answer:coefficient,the multiplier of a specified variable in a term

the multiplier of a specified variable in a term

Correct Answer:gradient,a measure of how steep a line is

a measure of how steep a line is

Correct Answer:intercept,the point where a line crosses a specified axis

the point where a line crosses a specified axis

Correct Answer:origin,the point with coordinates (0, 0)

the point with coordinates (0, 0)

Correct Answer:equation of a straight line,a relationship which, when plotted, forms a straight line

a relationship which, when plotted, forms a straight line

Q6.
Match each equation of a line to its key features.
Correct Answer:$$y = 3x − 2$$,gradient 3, $$y$$-intercept (0, -2)

gradient 3, $$y$$-intercept (0, -2)

Correct Answer:$$y = 3x + 2$$,gradient 3, $$y$$-intercept (0, 2)

gradient 3, $$y$$-intercept (0, 2)

Correct Answer:$$y = 2 - 3x$$,gradient -3, $$y$$-intercept (0, 2)

gradient -3, $$y$$-intercept (0, 2)

Correct Answer:$$y = 2x - 3$$,gradient 2, $$y$$-intercept (0, -3)

gradient 2, $$y$$-intercept (0, -3)

Correct Answer:$$y = 3 + 2x$$,gradient 2, $$y$$-intercept (0, 3)

gradient 2, $$y$$-intercept (0, 3)

Correct Answer:$$y = 3 - 2x$$,gradient -2, $$y$$-intercept (0, 3)

gradient -2, $$y$$-intercept (0, 3)

6 Questions

Q1.
Which of these descriptions best describes the gradient?
How much the $$x$$ values change for every 1 increase in $$y$$
Correct answer: 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 $$x$$
Q2.
The gradient of this line is .
An image in a quiz
Correct Answer: 3, three
Q3.
The gradient of this line is .
An image in a quiz
Correct Answer: -2, negative 2, negative two, minus 2, - 2
Q4.
The gradient of this line is .
An image in a quiz
Correct Answer: 5, five
Q5.
What is the equation of this line?
An image in a quiz
$$y=-{1\over 3}x - 2$$
$$y=-{1\over 3}x + 2$$
Correct answer: $$y={1\over 3}x - 2$$
$$y=3x - 2$$
$$y=2 - 3x$$
Q6.
Match each line to its correct equation.
An image in a quiz
Correct Answer:A (blue),$$y=-{2\over 3}x - 2$$

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

Correct Answer:B (pink),$$y=-{3\over 2}x - 2$$

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

Correct Answer:C (black),$$y={3\over 2}x $$

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

Correct Answer:D (green),$$y={3\over 2}x - 2$$

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

Correct Answer:E (purple),$$y={2\over 3}x - 2$$

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