Lets go back to our concept of equations.

To quickly review, an equation is when we set two expressions equal to each other.

We've discussed the idea of having a single variable in an equation, but what if we were to have 2?

This is where the concept of inputs and outputs come in.

If we were to plug in 1 for x we would get that y is equal to 7.

This means that the input is 1 and the output is 7.

If we were to plot the input on a number line it would look something like this :

This is the number line for x, the red dot highlighted is the input.

Now that we have an input, how would we represent an output? Would it be on the same line? Would we put it on a different number line? How would we connect inputs to outputs?

Well, there is an easy solution for this. We set up two number lines perpendicular to each other.

This is called a coordinate plane.

The coordinate plane solves all the problems that we previously discussed. It is able to show the relation between an input and an output.

We do this by first looking along the x-axis, the number line for our input.

*Note : It is helpful to make an indication of where your input is, in this case it is 1

Now look along the y-axis for your output, in this case it is 7.

But we're not done yet, we have to show that 7 is the output to the input of 1.

We can do this by finding where they intersect.

The mathematical way of representing this is by a point.

The green point drawn on the graph has the coordinates of (1,7)

To further break it down, the form we use to represent a point is (x, y)

Where :

• x is the input

• y is the output

In later lessons we will further explore the applications of a coordinate plane.