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

The gradient is a measure of how steep a line is.

An intercept is the coordinate where a line or curve meets a given axis.

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).

Problem solving with graphical representations

Maths

Checking and securing understanding of non-linear sequences

Extending thinking about sequences

Exploring the shapes of graphs using technology

Equations and their graphs

Efficiently drawing linear graphs

Reading from graphs

Modelling with graphs

Graphically solving two linear graphs that intersect

In this unit, pupils studied the graphical representation of a geometric sequence and linked features of the graph to its equation. In the future unit, other types of graphs are introduced and their key features identified.

In the prior unit, pupils considered geometric sequences and how they might be represented graphically. In this unit, pupils study the graphical representation to link features of the graph to its equation.

In this unit pupils draw, interpret and utilise linear graphs to solve problems. This knowledge is further extended to look at intersecting graphs.

Graphical representations

The y-{{}} is the point where a line or curve meets the $$y$$-axis.

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?

The graph models the time taken for three people to run 100 metres. Which line represents the fastest runner?

The parabola is used to model the throw of a tennis ball. The ball reaches a height of 10 metres {{ }} times.

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 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?

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 $$y=5-x$$.

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?

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 $$2x-9=3-x$$?

Use the graph to solve the simultaneous equations $$y=2x-1$$ and $$y=5-x$$.

The diagram shows 6 points and the the lines $$y=2x-1$$ and $$y=5-x$$. Which points satisfy the inequality $$y<5-x$$ ?

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 {{}}.

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 $$y=5-x$$.