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.

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

Equations and their graphs

Maths

Checking and securing understanding of non-linear sequences

Extending thinking about sequences

Exploring the shapes of graphs using technology

Efficiently drawing linear 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

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

Which of these graphs will NOT form straight line when plotted?

Identify the linear graphs with a gradient of 3.

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 $$y=9x-15$$ can be found just by looking at the equation?

Which of these equations could this sketch represent?

The graph of the linear equation $$y=5x-9$$ is uniquely defined by a gradient of $$5$$ and __________ of $$-9$$.

Which of these graphs will not form straight line when plotted?

Which of these will be $$y$$ values if you populated this table for values for the linear equation $$y=7-2x$$?

From left to right how will the $$y$$ values in this table be read if you complete the table for the linear equation $$y=4x-9$$?

The linear graph $$3x+5y=25$$ is plotted. When the $$x$$ coordinate is $$0$$ the $$y$$ coordinate is {{}}.

The quadratic graph of $$y=x^2$$ is plotted. When the $$x$$ coordinate is $$-5$$ the $$y$$ coordinate is {{}}.

Starter Quiz

The graph of the linear equation $$y=5x-9$$ is uniquely defined by a gradient of $$5$$ and __________ of $$-9$$.