We talked about imagining the relation between two numbers by sliding arrows up and down two lines. The example we chose was “the second number must be twice the first.”
This visual sliding of arrows is math. Now consider this: take those two lines and set them next to each other (at a 90-degree angle, or “orthogonally”) as shown above. The sliding arrows work the same way. Look familiar? This is the Cartesian Plane, or more simply an x-y plane. It’s how you graph numbers and equations.
See how the sliding arrows trace a dotted line? This is the equation y=2x. Or, said in plain English: The second number is twice the first. Choose x, double it, and you get y.
These plots you learn to make in algebra class are just ways to display relations that can also be said in plain words. Different people think different ways. Do you think of numbers visually, or as quantities?
