Any straight line on a graph can be represented algebraically by the equation y=mx+c

This equation relates x, i.e. the x-coordinates, with y, the y-coordinates.

But what are the other two letters that we see there, the constants m and c.

Well, consider when x=0. Then y=c. So c is the y-coordinate when x=0. Another way to say that is that it is the y-intercept, that is, the point where the graph crosses the y-axis.

As for m, it tells us how much the line goes up for every 1 that it goes across. We call it the gradient. If the gradient is 5, the line is very steep going upwards. If the gradient is -1/2, the gradient is not so steep and is going downwards.

There are special forms of this equation for horizontal lines and vertical lines. Horizontal lines will always have the equation y=c and vertical lines will always have the equation x=c.

Exercise

Let’s consolidate our understanding of straight line graphs by completing exercise 14I on pages 227 and 228 of the textbook:

The answers are below: