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Year 10
Higher

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.

icon-background-square
New
New
Year 10
Higher

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.
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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
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a term that does not vary

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

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

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

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

Correct Answer:equation of a straight line,a relationship which, when plotted, forms a straight line
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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)
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gradient 3, $$y$$-intercept (0, -2)

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

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

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

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

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

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

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

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

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