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

Efficiently drawing linear graphs

Maths

Checking and securing understanding of non-linear sequences

Extending thinking about sequences

Exploring the shapes of graphs using technology

Equations and their graphs

Reading from graphs

Modelling with graphs

Graphically solving two linear graphs that intersect

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

The minimum number of coordinates needed to plot the graph of a linear equation is {{ }}

Aisha is plotting the graph of the line $$y=2x+1$$. She only wants to plot two points. The first point Aisha plots is (0, 1). Which of these points would be the best second point for Aisha to use?

Sam plots the graph of the linear equation $$4x + 6y = 24$$. When $$x=0 $$ then $$y=$${{}}.

Match each pair of coordinates with the equation of the line that coordinates are on.

Jacob wants to draw the graph of $$y = 0.25x + 5.25$$ for positive values of $$x$$. The coordinates of the first point on the line that has positive integer coordinates are {{}}.

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

Which of these graphs will form straight line when plotted?

Identify the linear graphs with a gradient of 4.

These are all linear equations which give straight line graphs. Match each linear equation with another equation to form a pair of parallel lines.

What features of the graph of $$y=5-7x$$ can be found just by looking at the equation?

Which of these equations could this sketch represent?

Efficiently drawing linear graphs

Lesson outcome