Connecting The Cartesian Plane with Algebra.

So far, the Cartesian Plane doesn't seem much more interesting than a mathematical version of a map. However, the very radical thing that Descartes did was to connect mathematical equations, from algebra, with this Cartesian Plane. He did this by making a connection between the variable names of the axes lines on the Cartesian Plane, and the variable names in a mathematical equation.

Let's consider how this works.

Descartes very simply said that you could match up a variable name in an equation with a one of the axes lines in the Cartesian Plane. For example, if you have an equation with the variable 'x' in it, you can match this variable in the equation to the x axis on the Cartesian plane.

For example, suppose you have the equation x = 4 - 1. In this case, you could match the variable name x with the line named x (the x axis) on the Cartesian Plane.


Then, you could match the number value of the variable x at a particular time with its particular number label on the x axis. In this case, we have

x = 4 - 1
x = 3

In order for this to be a TRUE statement, the value of the variable x must be 3, so you can match the value of x up with the 3 on the x axis.
 

Now suppose you had the variable name y in an equation y = 5 + 1, and you matched the variable y up with the y axis.

Question: What is the value of y, according to the equation (Answer 1)
Question: How would you match this up with the Cartesian Plane? (Answer 2)