Problem solving with graphical representations | Maths

Starter quiz

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 $y=5-x$ .
- intersecting
- non-linear
- quadratic
- simultanous ✓
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?
- '0' ✓
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 $2x-9=3-x$ ?
- $x=-1$
- $x=4$
- $y=-1$
- $y=4$
Use the graph to solve the simultaneous equations $y=2x-1$ and $y=5-x$ .
- $x=3$ , $y=2$
- $x=7$ , $y=-2$
- $x=1$ , $y=1$
- $x=-2$ , $y=7$
- $x=2$ , $y=3$ ✓
The diagram shows 6 points and the the lines $y=2x-1$ and $y=5-x$ . Which points satisfy the inequality $y<5-x$ ?
- A ✓
- C
- D
- F ✓
- B and E
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 ______.
- 'C' ✓

Exit quiz

The y-______ is the point where a line or curve meets the $y$ -axis.
- 'intercept' ✓
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?
- Alex says $x=2$ , $y=3$ ✓
- Izzy says $x=-2$ , $y=-3$ ✓
- Jun says $x=2$ , $y=-3$
- Laura says $x=-2$ , $y=3$ ✓
The graph models the time taken for three people to run 100 metres. Which line represents the fastest runner?
- Line a ✓
- Line b
- Line c
The parabola is used to model the throw of a tennis ball. The ball reaches a height of 10 metres ______ times.
- '2' ✓
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.
- A
  
  ⇔
  
  Laura is accelerating ✓
- B
  
  ⇔
  
  Laura is running fast ✓
- C
  
  ⇔
  
  Laura is slowing down ✓
- D
  
  ⇔
  
  Laura has nearly stopped ✓
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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Lesson Details

Key learning points

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

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.

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).