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Year 9

Equations and their graphs

I can recognise the determining features of the shape of the graph from its equation.

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New
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Year 9

Equations and their graphs

I can recognise the determining features of the shape of the graph from its equation.

Download all resources
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Share activities with pupils
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Lesson details

Key learning points

  1. The gradient of the line is determined by m when the equation is in the form y = mx + c
  2. The y-intercept is determined by c when the equation is in the form y = mx + c
  3. You can sketch what the graph will look like from studying its equation

Keywords

  • Gradient - The gradient is a measure of how steep a line is.

  • Intercept - An intercept is the coordinate where a line or curve meets a given axis.

  • Linear - The relationship between two variables is linear if, when plotted on a pair of axes, a straight line is formed.

Common misconception

Estimation and approximation are only required skills when working solely with number problems.

In problem solving it can be really useful to sketch an approximation of a certain graph such as a linear equation. Seeing where the $$y$$-intercept is and drawing an approximate gradient could help us identify solutions.

In pairs, ask pupils to come up with their own linear graphs and challenge their peers to sketch them. Accurately sketching multiple linear equations on the same axes is a valuable skill.
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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Starter quiz

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6 Questions

Q1.
The graph of the linear equation $$y=5x-9$$ is uniquely defined by a gradient of $$5$$ and __________ of $$-9$$.
$$y$$-axis
$$y$$ coordinate
Correct answer: $$y$$ intercept
$$y$$ solution
Q2.
Which of these graphs will not form straight line when plotted?
$$y=7x-2$$
$$y=2-7x$$
Correct answer: $$y=x^2-7$$
$$y=-2x-7$$
$$7x+2y=1$$
Q3.
Which of these will be $$y$$ values if you populated this table for values for the linear equation $$y=7-2x$$?
An image in a quiz
-2
Correct answer: 1
2
Correct answer: 7
Correct answer: 9
Q4.
From left to right how will the $$y$$ values in this table be read if you complete the table for the linear equation $$y=4x-9$$?
An image in a quiz
-3, -2, -1, 0, 1, 2, 3
-17, -13, -9, -5, -1, 3, 7
-21, -25, -29, -33, -37, -41, -45
Correct answer: -21, -17, -13, -9, -5, -1, 3
3, -1, -5, -9, -13, -17, -21
Q5.
The linear graph $$3x+5y=25$$ is plotted. When the $$x$$ coordinate is $$0$$ the $$y$$ coordinate is .
Correct Answer: 5, y=5, +5
Q6.
The quadratic graph of $$y=x^2$$ is plotted. When the $$x$$ coordinate is $$-5$$ the $$y$$ coordinate is .
Correct Answer: 25, y=25, +25

Exit quiz

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6 Questions

Q1.
An __________ is the coordinate where a line or curve meets a given axis.
intersection
Correct answer: intercept
inverse
Q2.
Which of these graphs will NOT form straight line when plotted?
$$y=7x-3$$
$$y=3-7x$$
Correct answer: $$y=x^3-7$$
$$y=-3x-7$$
$$7x+y=1$$3
Q3.
Identify the linear graphs with a gradient of 3.
Correct answer: $$y=3x-3$$
$$y=x+3$$
$$y=7-3x$$
Correct answer: $$y=3x+7$$
Correct answer: $$y=11+3x$$
Q4.
These are all linear equations which give straight line graphs. Match each linear equation with another equation to form a pair of parallel lines.
Correct Answer:$$y=5x-7$$,$$y=5x+18$$

$$y=5x+18$$

Correct Answer:$$y=3-2x$$,$$y=-2x+7$$

$$y=-2x+7$$

Correct Answer:$$y=-4+2x$$,$$y=2x-7$$

$$y=2x-7$$

Correct Answer:$$y=7x-10$$,$$y=7x$$

$$y=7x$$

Correct Answer:$$y=7-x$$,$$y=-2-x$$

$$y=-2-x$$

Q5.
What features of the graph of $$y=9x-15$$ can be found just by looking at the equation?
Correct answer: It is a straight line graph.
Correct answer: It has a gradient of $$9$$
It has a gradient of $$-15$$
It has a $$y$$-intercept of $$9$$
Correct answer: It has a $$y$$-intercept of $$-15$$
Q6.
Which of these equations could this sketch represent?
An image in a quiz
Correct answer: $$y=9x-15$$
$$y=9x+15$$
$$y=15-9x$$
Correct answer: $$y=19x-156$$
$$y=19x$$