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

A quadratic is a an equation, graph, or sequence whereby the highest exponent of the variable is 2.

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).

Reading from 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

Efficiently drawing linear 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 graph of a {{}} equation is called a parabola.

Use the graph of $$y =3x-4$$ to solve the equation $$3x-4=8$$. The solution is $$x=$${{}}.

Use the graph of $$y =7.4 x+12.95$$ to estimate the value of $$7.4\times 3+12.95$$. 

How many solutions are there to the equation $$x^2+2=10$$. Use the graph of $$y=x^2+2$$ to help you. 

Use the graph of $$y=\frac{1}{2} x^2+1$$ to help you solve the equation $$\frac{1}{2}x^2+1=3$$.

This parabola models the flight of a cricket ball being thrown. The cricket ball is above a height of 5 metres for a distance of {{ }} metres altogether.

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

What is the minimum number of coordinates needed to plot the graph of $$y=5x+3$$ ?

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

Laura is plotting the graph of the line $$3y + 5x=15$$. She only wants to plot two points. Which of these points would be the best points for Laura to use?

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

Jun wants to draw the graph of $$y = 0.2x + 2.2$$ for positive values of $$x$$. The coordinates of the first point on the line that has positive integer coordinates are {{}}.

Reading from graphs

Lesson outcome