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Lesson details

Learning outcome

I can read and interpret points from a graph to solve problems.

Key learning points

  1. If you have one value, you can use a linear graph to find its pair.
  2. The pair of values will satisfy the linear equation.
  3. If the x and y variables have context, then their values can be interpreted within that context.
  4. With quadratic graphs, there may be more than one value to find.

Keywords

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

  • Quadratic - A quadratic is a an equation, graph, or sequence whereby the highest exponent of the variable is 2.

  • Parabola - A parabola is a curve where any point on the curve is an equal distance from a fixed point (the focus) and a fixed straight line (the directrix).

Common misconception

Since linear equations (typically) have one solution, all equations have one solution.

Ask pupils to compare the graphical solution to a linear equation with the graphical solution to a quadratic equation. This will enable them to see that it is possible for a quadratic equation to have more than one solution.

Teacher tip

After using the graph of y=20x-0.4 to calculate 20 x 0.06 - 0.4 challenge pupils to read as many accurate calculations as they can from that same graph.

Licence

This content is © Oak National Academy Limited (2025), 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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Prior knowledge starter quiz

6 Questions

Q1.
The relationship between two is linear if, when plotted on a pair of axes, a straight line is formed.

Correct Answer: variables

Q2.
What is the minimum number of coordinates needed to plot the graph of $$y=5x+3$$ ?

1
Correct answer: 2
3
4
5

Q3.
Andeep plots the graph of the linear equation $$4x + 6y = 24$$. When $$y=0 $$ then $$y=$$ .

Correct Answer: 6

Q4.
Laura is plotting the graph of the line $$3y + 5x=15$$. She only wants to plot two points. Which of these points would be the best points for Laura to use?

Correct answer: When $$x=0$$
When $$x=1$$
When $$x=2$$
Correct answer: When $$x=3$$
When $$x=4$$

Q5.
Match each pair of coordinates with the equation of the line that coordinates are on.

Correct Answer:$$(3, 0)$$,$$y=2x-6$$

$$y=2x-6$$

Correct Answer:$$(3, 1)$$,$$3y=x$$

$$3y=x$$

Correct Answer:$$(3, 2)$$,$$x+y=5$$

$$x+y=5$$

Correct Answer:$$(3, 3)$$,$$y=x$$

$$y=x$$

Correct Answer:$$(3, 4)$$,$$2y-3x=-1$$

$$2y-3x=-1$$

Q6.
Jun wants to draw the graph of $$y = 0.2x + 2.2$$ for positive values of $$x$$. The coordinates of the first point on the line that has positive integer coordinates are .

Correct Answer: (4, 3), (4,3)

6 Questions

Q1.
The graph of a equation is called a parabola.

Correct Answer: quadratic

Q2.
Use the graph of $$y =3x-4$$ to solve the equation $$3x-4=8$$. The solution is $$x=$$ .

An image in a quiz
Correct Answer: 4, four

Q3.
Use the graph of $$y =7.4 x+12.95$$ to estimate the value of $$7.4\times 3+12.95$$.

An image in a quiz
25
30
Correct answer: 35
40
45

Q4.
How many solutions are there to the equation $$x^2+2=10$$. Use the graph of $$y=x^2+2$$ to help you.

An image in a quiz
0
1
Correct answer: 2
3
Infinite

Q5.
Use the graph of $$y=\frac{1}{2} x^2+1$$ to help you solve the equation $$\frac{1}{2}x^2+1=3$$.

An image in a quiz
Correct answer: $$x=-2$$
$$x=-1$$
$$x=1$$
Correct answer: $$x=2$$
$$x=3$$

Q6.
This parabola models the flight of a cricket ball being thrown. The cricket ball is above a height of 5 metres for a distance of metres altogether.

An image in a quiz
Correct Answer: 16, sixteen

To help you plan your 9 maths lesson on: Reading from graphs, download all teaching resources for free and adapt to suit your pupils' needs...