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Year 9

Efficiently drawing linear graphs

I can draw a linear graph efficiently and accurately.

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New
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Year 9

Efficiently drawing linear graphs

I can draw a linear graph efficiently and accurately.

Download all resources
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Share activities with pupils
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Lesson details

Key learning points

  1. By choosing pairs of values that satisfy the equation, you can draw it accurately.
  2. For linear graphs, only two pairs of coordinates are required.
  3. The distance between the points should not be too small.

Keywords

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

Common misconception

A table of values should always be filled in and all points plotted in order to graph a linear equation.

A linear equation will form a straight line graph therefore we only need to know two points in order to draw the line.

When plotting just two points to draw a linear graph, encourage pupils to try plotting using two neighbouring points, and then using two distant points. This will allow them to experience how much easier and more accurate the latter method is.
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 $$$$- is the point where a line or curve meets the $$y$$-axis.
Correct Answer: intercept, Intercept
Q2.
Which of these graphs will form straight line when plotted?
Correct answer: $$y=2x+3$$
$$y=2x^3+3$$
$$y=3x^2+3$$
Correct answer: $$y=3x-2$$
Correct answer: $$y+2x=3$$
Q3.
Identify the linear graphs with a gradient of 4.
Correct answer: $$y=4x-3$$
$$y=x+4$$
$$y= 3 - 4x$$
$$y=4x^3$$
Correct answer: $$y=3+4x$$
Q4.
These are all linear equations which give straight line graphs. Match each linear equation with another equation to form a pair of parallel lines.
Correct Answer:$$y=5x+2$$,$$y=2+5x$$

$$y=2+5x$$

Correct Answer:$$y=5-2x$$,$$y=-2x+5$$

$$y=-2x+5$$

Correct Answer:$$y=2x$$,$$y=2x+5$$

$$y=2x+5$$

Correct Answer:$$y=x-5$$,$$y=x-2$$

$$y=x-2$$

Correct Answer:$$y=2-x$$,$$y=-x-5$$

$$y=-x-5$$

Q5.
What features of the graph of $$y=5-7x$$ can be found just by looking at the equation?
It has a gradient of $$7$$
Correct answer: It has a gradient of $$-7$$
Correct answer: It has a $$y$$-intercept of $$5$$
It has a $$y$$-intercept of $$-7$$
Correct answer: It is a straight line.
Q6.
Which of these equations could this sketch represent?
An image in a quiz
$$y=3x-8$$
Correct answer: $$y=8x+3$$
$$y=8-3x$$
$$y+8x=3$$
Correct answer: $$y-3x=8$$

Exit quiz

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6 Questions

Q1.
The relationship between two variables is if, when plotted on a pair of axes, a straight line is formed.
Correct Answer: linear
Q2.
The minimum number of coordinates needed to plot the graph of a linear equation is
Correct Answer: 2, two, Two, TWO
Q3.
Aisha is plotting the graph of the line $$y=2x+1$$. She only wants to plot two points. The first point Aisha plots is (0, 1). Which of these points would be the best second point for Aisha to use?
(0.1, 1.2)
(0.5, 1.5)
(3, 5)
Correct answer: (5, 11)
(1000, 2001)
Q4.
Sam plots the graph of the linear equation $$4x + 6y = 24$$. When $$x=0 $$ then $$y=$$ .
Correct Answer: 4
Q5.
Match each pair of coordinates with the equation of the line that coordinates are on.
Correct Answer:$$(2, 3)$$,$$x+y=5$$

$$x+y=5$$

Correct Answer:$$(2, 4)$$,$$2y-x=6$$

$$2y-x=6$$

Correct Answer:$$(2, 1)$$,$$y+2x=5$$

$$y+2x=5$$

Correct Answer:$$(2, 5)$$,$$y-2x=1$$

$$y-2x=1$$

Correct Answer:$$(2, 2)$$,$$2y+x=6$$

$$2y+x=6$$

Q6.
Jacob wants to draw the graph of $$y = 0.25x + 5.25$$ for positive values of $$x$$. The coordinates of the first point on the line that has positive integer coordinates are .
Correct Answer: (3, 6), (3,6), 3,6, 3, 6