New
New
Year 9

Reading from graphs

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

New
New
Year 9

Reading from graphs

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

Lesson details

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.

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.

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).

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.
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).

Loading...

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