Graphs & Equations

I often find that students work very hard at getting their head around equations and work equally hard on graphs. More often than not, they don't realise that equations and graphs are in fact two ways of saying the same thing.

Think about it - in an equation you have a relationship between two unknowns (we would usually call them x and y). The idea is that if you know what one of them is (say, you know x) then you can use the rule that the equation gives you to find out the other unknown.

For example, if your equation is y = 2x - 4 and you know that x is 5, then you follow the rule, which in this case says double it and then subtract 4 to tell you that y =6. On the other hand, if you had a graph of y = 2x -4, and you know that x is 5, you look up on the graph what y must be when x is 5. You get the same answer, y is 6.

This is big. Most of Maths interlinks when you see it. On a graph you can pick any point on the line and look up the co-ordinates. When you put the x and y co-ordinates in your equation then the equation must be true. It works for anywhere on the line. It doesn't work anywhere else.

Try it. Draw the graph of y = x-1. Pick some points on this graph. Try putting the x and y values in the equation y = x - 1. Do you notice that it is only when you pick points on the line that it works?

It's pretty clever really.

The graph and the equation do exactly the same thing. One of them is written as a rule, the other more like a diagram, but they are just different ways of expressing the relationship between two unknown quantities.