y = mx + c is an important real-life equation. The gradient, m, represents rate of change (eg, cost per concert ticket) and the y-intercept, c, represents a starting value (eg, an admin. fee).

Plotting the coordinates and drawing a line through them gives:

This is the graph of \(y = 3x - 1\).

Sketching straight line graphs

If you recognise that the equation is that of a straight line graph, then it is not actually necessary to create a table of values.

Just two points are needed to draw a straight line graph, although it is a good idea to do a check with another point once you have drawn the graph.

Example

Draw the graph of \(y = 3x - 1\).

If you recognise this as a straight line then just choose two ‘easy’ values of \(x\), work out the corresponding values of \(y\) and plot those points.