The Plot Thickens

Doing maths looking at equations all day can sometimes get boring. Maths gets a lot more interesting when there are pictures. Most pictures in math involve graphs, so let’s start simple and begin with plotting points on a graph.

You are familiar with the number line:

You already know how to plot a point on this. But this is only a 1-dimensional plot. The most interesting thing you can plot on this is a horizontal line which represent all the numbers between the endpoints of the line. Wouldn’t it be nice if we could plot curves in 2-dimensions! Enter the cartesion coordinate system.

To the number line, let’s add a vertical number line intersecting the horizontal one at 0:

Each of these number lines are called an axis. The horizontal one is called the x-axis and the vertical one is called the y-axis. Now you can plot a point on any of these axes, but the strength of this system is that you can plot points anywhere on the surface that the coordinate system is on. But to plot a point in 2-dimensions, you need 2 numbers.

The typical way to indicate a point in maths is by using brackets. For example: (2, 1), (0, -7), (-4,3), (-1.5, -2.75). By convention, the first number is the x coordinate and the second number is the y coordinate, so the general point is (x, y). To plot a point, say (2, 1), you first go along the x axis 2 units to the right since 2 is positive, then go up 1 unit. That’s where the point (2, 1) is. I’ve plotted several other points below:

The point (0, 0) where the axes meet is called the origin. Note that positive x values are to the right of the origin and positive y values are above the origin. Negative values are to the left and below respectively.

Now this is cool but gets quickly boring just plotting points. The interesting things happen when we plot a set of points that satisfy an equation. I’ll get into that in my next post.