1. 9
Graphs and Graphing

2. R.1 Fractions
9.4 The Rectangular Coordinate System
Objectives
Plot a point, given the coordinates, and find the coordinates, given a point.
Identify the four quadrants and determine which points lie within each one.

3. Plot a point, given the coordinates, and find the coordinates, given a point.
The line graph below shows the relationship between two things. This is an example of paired data.
Months are shown on
the horizontal axis.
Number of trout shown
on the vertical axis.
Paired Data:

4. Plot a point, given the coordinates, and find the coordinates, given a point.
The rectangular coordinate system is made up of a horizontal axis (called the x-axis) and a vertical axis (called the y-axis).

5. Move right along the horizontal x-axis to 3.
Plot a point, given the coordinates, and find the coordinates, given a point.
Plot the point (3, 5).
Example
Move right along the horizontal x-axis to 3.
Move up 5 units until aligned with the 5 on the vertical y-axis.
(3, 5)

6. Move right along the horizontal x-axis to 4.
Plot a point, given the coordinates, and find the coordinates, given a point.
Plot the point (4, –2).
Example
Move right along the horizontal x-axis to 4.
Move down 2 units until aligned with the –2 on the vertical y-axis.
(4, –2)

7. Move left along the horizontal x-axis to –2.
Plot a point, given the coordinates, and find the coordinates, given a point.
Plot the point (–2, 4).
Example
Move left along the horizontal x-axis to –2.
Move up 4 units until aligned with the 4 on the vertical y-axis.
(–2, 4)

8. Move left along the horizontal x-axis to –3.
Plot a point, given the coordinates, and find the coordinates, given a point.
Plot the point (–3, 0).
Example
Move left along the horizontal x-axis to –3.
The 0 indicates that we do not move along the vertical y-axis.
The point is plotted on the x-axis.
(–3, 0)

9. The 0 indicates that we do not move along the horizontal x-axis.
Plot a point, given the coordinates, and find the coordinates, given a point.
Plot the point (0, –5).
Example
The 0 indicates that we do not move along the horizontal x-axis.
Move down 5 units to the –5 on the vertical y-axis.
The point is plotted on the y-axis.
(0, –5)

10. Plot a point, given the coordinates, and find the coordinates, given a point.
Find the coordinates of points A, B, C, and D.
Example
A: move right 4 and up 1
(4, 1)
B: move left 4 and up 3
(–4, 3)
C: move right 2 and down
(2, – )
D: only move left 1
(–1, 0)

11. Identify the four quadrants and determine which points lie within each one.
The x-axis and y-axis divide the coordinate system into four regions, called quadrants.

12. Identify the four quadrants and determine which points lie within each one.
Provide an example of two points that lie in quadrant III.
Example
Points in quadrant III have the pattern (–, –).
(–2, –5) and (–3, –3)

13. Identify the four quadrants and determine which points lie within each one.
Example
Identify the quadrants in which each point located? (3, 5) (1, –6) (–4, 0)
The pattern for (3, 5) is (+, +), so it is in quadrant I.
The pattern for (1, –6) is (+, –), so it is in quadrant IV.
(–4, 0) is on the x-axis, so it does not lie in any quadrant.