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).