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

Graphically solving two linear graphs that intersect

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

Problem solving with graphical representations

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 point where the lines $$y=2x+4$$ and $$y=2-x$$ meet is called the {{ }}.

Izzy plots the graphs of $$y=2x+1$$ and $$y=3x-2$$ on the same coordinate grid. How many points will lie on both lines?

The linear equations $$y = 2x + 5$$ and $$y = 2 − x$$ intersect at the point with coordinates (−1, 3). What is the solution to the equation $$2x+5=2-x$$?

Use the graph to solve the simultaneous equations $$y=2x-1$$ and $$y=3x-2$$.

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

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 {{}}.

The graph of a __________ equation is a straight line.

Which of these lines has the least steep gradient?

Use the graph of $$y =3x-4$$ to solve the equation $$3x-4=2$$. The solution is $$x=$${{}}.

Use the graph of $$y =7.4 x+12.95$$ to estimate the value of $$7.4\times 4+12.95$$. 

Aisha is plotting the graph of the line $$3y + 4x=24$$. She only wants to plot two points. Which of these points would be the best points for Aisha to use?

Select the points which lie both on the line $$y=2x+1$$ and on the line $$y=3x-2$$.

Graphically solving two linear graphs that intersect

Lesson outcome