Matching up Two Variables

Since there are two lines (the axes) on the Cartesian Plane, you can match equations that have two variables in them up with the two axes of the plane. You might think that only being able to match up two variable names with the plane would limit it's usefulness, but it turns out that it is quite useful in a variety of real world situations.

When you are dealing with two variables, you match up your variables with the Cartesian plane a bit differently than in the single variable examples in section 4.3. To see what you do in the case of two variables, consider the following example.

Suppose Andrew was entered in an Arctic Sports competition, in the One Foot High Kick.

On his first try he kicked 2 meters high, and missed the target. On his second try, he kicked 2.2 meters high, and missed the target. On his third try he kicked 2.3 meters and hit the target.

Now suppose we use the variable name TurnNumber to name the turns, and the variable name HeightKicked to name the height that Andrew kicked on each turn.

We can list the information in a chart to see it more clearly:

 TurnNumber HeightKicked 1 2 2 2.2 3 2.3

To connect this situation, with its two variables, to the Cartesian Plane, we can match each variable up with one of the axes on the plane. Since our variables aren't named x and y this time, we need to give the x axis and y axis nick-names that match up with the variable names we do have. For instance, we can match the TurnNumber variable up with the x axis and call this axis TurnNumber and the HeightKicked variable up with the y axis, and call this axis HeightKicked.

To see what I mean by this, let's consider the situation when

TurnNumber = 1

and

HeightKicked = 2

In this case, we are going out by a length of 1 on the x axis (because we've matched TurnNumber up with the x axis) and out by a length of 2 on the y axis (because we've matched HeightKicked up with the y axis). As discussed in section 4.2 this will get us to the point labelled (1, 2) on the Cartesian plane (see picture below).

Similarly, when

TurnNumber = 2

and

HeightKicked = 2.2

We can match the variables up with the point labelled (2, 2.2) on the Cartesian plane

Question: For the last turn, how would you match the values of the variables TurnNumber and HeightKicked up with a point on the Cartesian Plane? Draw a Cartesian plane and mark a point for each of the three turns. (Answer 1)