The Cartesian Plane And You

1
The Cartesian Plane And You!

• Remember our number line?

We were able to use our number line to Example
Plot a single point x 3 Graph
inequalities with a single variable x 7 But
what about equations with two variables? y 2x
- 7 How can we graph those?
2
Descartes Strikes Back!

• A famous French mathematician named Rene
  Descartes gave us the necessary means by which to
  visualize equations with two variables.

Math rules!
3
The Coordinate Plane

• Think of it as two number lines that overlap each
  other in the middle

• KEY FACTS
• Vertical Axis y axis
• Horizontal Axis x axis
• Goes on forever in both directions

4
So how does it work?

• Now that we have TWO axes, we need to name points
  using TWO numbers!

Every point is of the form (x, y) x
x-coordinate (How far right or left) y
y-coordinate (How far up or down)
5
Time for Examples

• Suppose I wanted to graph the point (3, 4)

I start at the center. Then I have to walk 3
spaces to the right and 4 spaces up.
(3, 4)
walked four spaces up
walked three spaces to the right
6
You try some!

• Graph the following points
• (2, 3)
• (1, 4)
• (0, 0)

Remember, we walk right first, and then we walk
up!
7
Howd we do?

• Hopefully, you got these three points.

(1,4)
(2,3)
(0,0)
Key Fact (0,0) is a very special point on our
graph. Its also called the origin.
8
What about those pesky negatives?

• You may have noticed that all of our points so
  far have been in the upper right hand corner of
  our graph. So how do we land somewhere else?

9
Negative Coordinates

• Suppose I ask you to plot (-3, -1). What does
  that mean?
• It just means that now I walk 3 spaces to the
  LEFT and 1 space DOWN.
• This is what the negative does - it forces you to
  walk in the opposite direction!

(-3, -1)
10
Your turn!

• Plot the following points
• (-4, -2)
• (-2, 3)
• (3, -1)

Remember If the x-coordinate is negative, we
walk left. If the y-coordinate is negative, we
walk down.
11
Howd we do?

• Hopefully, you got these points.

(-2, 3)
(3, -1)
(-4, -2)
12
Quadrant Quandary

• Notice that our graph really has four parts to
  it. Well, we have a name for those parts.
  Theyre called quadrants.
• We name them using Roman Numerals.
• Each quadrant has a special property about its
  coordinates.

x is positive y is positive
x is negative y is positive
(-x, y)
(x, y)
I
II
IV
III
(-x, -y)
(x, -y)
x is negative y is negative
x is positive y is negative