breakeven_graph.jpgLinear functions have graphs which are straight lines.

The general equation of a linear function is ax + by + c = 0.

The exponents of both the x term and the y term are 1.

Another often used form of linear functions is y = mx + c.


The gradient of a straight line is a measure of its slope.

The gradient, m is defined as:





Sketching Straight Line Graphs

There are several ways to sketch the graphs of linear functions.

Intercept method.

Find the two intercepts by putting x = 0 into the equation and finding the corresponding y value.

Then put y = 0 into the equation and find the corresponding x value.

This gives the values of x and y where the graph cuts the axes.

e.g. 3x + 2y = 6

Put x = 0
3 x 0 + 2y = 6
2y = 6
y = 3
The y-intercept is 3.

Put y = 0
3 x + 2 x 0 = 6
3x = 6
x = 2
The x-intercept is 2.




Gradient / Intercept method.

If the equation is written in the form y = mx + c, where y is the subject of the equation, then:

m, the coefficient of x, is the gradient of the line,

and c, the constant term, is the y-intercept.

e.g. y = 2x + 1

By inspection of the above equation:

Gradient is 2

y-intercept is 1


Types of Lines

Type of lines
Vertical lines These have equations of the type x = a x = 3 or x = -2
Horizontal lines These have equations of the type y = b y = 6 or y = -3
Lines through origin These have equations of the type y = mx y = 3x or y = -2x