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)
Answers
Answer 1: