Mathematicans normally get their "kicks" from viewing curvaceous figures in graphical format rather than whilst playing "Tomb Raider" oddly enough!

The main way to show how equations are related the numbers which satisfy them (make the equations true) is by drawing graphs. A little time spent becoming familiar with the shapes of several types of graphs will pay you huge dividends later when you need to answer questions on them in exams.

"A picture paints a thousand words" is commonly quoted. This is true in maths also. Where algebraic equations are used in research papers (all you "rocket scientists" out there!) and in business proposals etc. they will always be accompanied with supporting graphs so that people can quickly visualise what you are talking about.

Here are examples of the main types of graph:

Linear Equations
Anything which is linear relates to a straight line and so do the graphs of linear equations.
The general equation for these graphs is y = mx + c.

Point to remember:
m represents the gradient of the graph and
c is the point where the graph crosses the y-axis (vertical axis).

The gradient (also called the slope) tells you how steep the graph is.

Quadratic Equations
These graphs are n or u shaped curves (also called parabolas). They are all symmetrical about a vertical line down the centre of the graph. They have one turning point (this is where the graph alters direction - like going round a corner).
The general equation for these graphs is y = ax² + bx + c. See the tutorial on quadratic equations for more on this.

Cubic Equations
Cubic graphs should have up to two turning points.
The general equation for these graphs is y = ax³ + bx² + cx + d.

Reciprocal Equations
These graphs are all called hyperbolas. This means they consist of two separate lines which are opposite each other as though they were a reflection of each other.
The general equation for these graphs is y = a / x.