New
New
Year 9

Problem solving with graphical representations

I can use my knowledge of graphical representations to solve problems.

New
New
Year 9

Problem solving with graphical representations

I can use my knowledge of graphical representations to solve problems.

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Lesson details

Key learning points

  1. When presented with a real-life problem, it can help to sketch what is happening.
  2. A sketch can provide a visual aid for understanding.
  3. In there is a context to the problem then the solution should be given in context.

Keywords

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

  • 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.

  • 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

A distance time graph will always be constructed with straight lines.

A straight line represents a consistent rate of a change, a consistent speed. In reality we need to model acceleration and deceleration which will involve curved lines.

In each case, encourage pupils to verbalise what it is that the sketch shows them.
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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6 Questions

Q1.
The diagram shows the lines $$y=2x-1$$ and $$y=5-x$$. The point A will help you find the solution to the __________ equations $$y=2x-1$$ and $$y=5-x$$.
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intersecting
non-linear
quadratic
Correct answer: simultanous
Q2.
Sam plots the graphs of $$y=3x+1$$ and $$y=3x-4$$ on the same coordinate grid. How many points will lie on both lines?
Correct Answer: 0, zero, none
Q3.
The linear equations $$y = 2x -9$$ and $$y = 3 − x$$ intersect at the point with coordinates (4, -1). What is the solution to the equation $$2x-9=3-x$$?
$$x=-1$$
$$x=4$$
$$y=-1$$
$$y=4$$
Q4.
Use the graph to solve the simultaneous equations $$y=2x-1$$ and $$y=5-x$$.
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$$x=3$$, $$y=2$$
$$x=7$$, $$y=-2$$
$$x=1$$, $$y=1$$
$$x=-2$$, $$y=7$$
Correct answer: $$x=2$$, $$y=3$$
Q5.
The diagram shows 6 points and the the lines $$y=2x-1$$ and $$y=5-x$$. Which points satisfy the inequality $$y<5-x$$ ?
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Correct answer: A
C
D
Correct answer: F
B and E
Q6.
The diagram shows 6 points and the the lines $$y=2x-1$$ and $$y=5-x$$. The point that is the region $$y>5-x$$ and $$y>2x-1$$ is .
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Correct Answer: C, c

6 Questions

Q1.
The y- is the point where a line or curve meets the $$y$$-axis.
Correct Answer: intercept
Q2.
Four pupils are solving a pair of simultaneous equations. The diagram shows the graphs of the equations they are solving. Which pupils are definitely incorrect?
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Correct answer: Alex says $$x=2$$, $$y=3$$
Correct answer: Izzy says $$x=-2$$, $$y=-3$$
Jun says $$x=2$$, $$y=-3$$
Correct answer: Laura says $$x=-2$$, $$y=3$$
Q3.
The graph models the time taken for three people to run 100 metres. Which line represents the fastest runner?
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Correct answer: Line a
Line b
Line c
Q4.
The parabola is used to model the throw of a tennis ball. The ball reaches a height of 10 metres times.
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Correct Answer: 2, twice
Q5.
The graphs models Laura running a 100 metre race. The graph covers a distance of 110 metres. Match each section of the graph to the correct statement.
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Correct Answer:A,Laura is accelerating

Laura is accelerating

Correct Answer:B,Laura is running fast

Laura is running fast

Correct Answer:C,Laura is slowing down

Laura is slowing down

Correct Answer:D,Laura has nearly stopped

Laura has nearly stopped

Q6.
A container is filled with water at a constant rate. The graph shows the depth of water in a container as it is filled. Which of these could be a cross section of the container?
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An image in a quiz
An image in a quiz
An image in a quiz
Correct Answer: An image in a quiz
An image in a quiz