1. Chapter 3
Graphing

2. Reading Graphs and the Rectangular Coordinate System
§ 3.1
Reading Graphs and the Rectangular Coordinate System

3. Bar Graphs
A bar graph consists of a series of bars arranged vertically or horizontally.
The following bar graph shows the attendance at each Super Bowl game from 2000 to 2007.

4. Line Graphs
A line graph consists of a series of points connected by a line. It is also sometimes called a broken line graph.
The following line graph shows the attendance at each Super Bowl game from 2000 to 2007.

5. The Rectangular Coordinate System
Ordered pair – a sequence of two numbers where the order of the numbers is important
Origin – point of intersection of two axes
Quadrants – regions created by intersection of two axes
Axis – horizontal or vertical number line
The location of a point residing in the rectangular coordinate system created by a horizontal (x-) axis and vertical (y-) axis can be described by an ordered pair. Each number in the ordered pair is referred to as a coordinate.

6. Graphing an Ordered Pair
To graph the point corresponding to a particular ordered pair (a, b), you must start at the origin and move a units to the left or right (right if a is positive, left if a is negative), then move b units up or down (up if b is positive, down if b is negative).

7. Graphing an Ordered Pair
x-axis
y-axis
(5, 3)
5 units right
3 units up
(0, 5)
(-6, 0)
(2, -4)
(-4, 2)
(0, 0)
Quadrant I
Quadrant IV
Quadrant III
Quadrant II
origin
Note that the order of the coordinates is very important, since (– 4, 2) and (2, – 4) are located in different positions.

8. Graphing Paired Data
Paired data is data that can be represented as an ordered pair.
A scatter diagram is the graph of paired data as points in the rectangular coordinate system.
An order pair is a solution of an equation in two variables if replacing the variables by the appropriate values of the ordered pair results in a true statement.

9. Solutions of an Equation
Example:
Determine whether (3, – 2) is a solution of 2x + 5y = – 4.
Let x = 3 and y = – 2 in the equation.
2x + 5y = – 4
2(3) + 5(–2) = – Replace x with 3 and y with –2.
6 + (–10) = – Simplify.
– 4 = – True
So (3, –2) is a solution of 2x + 5y = – 4.

10. Solutions of an Equation
Example:
Determine whether (– 1, 6) is a solution of 3x – y = 5.
Let x = – 1 and y = 6 in the equation.
3x – y = 5
3(– 1) – 6 = Replace x with – 1 and y with 6.
– 3 – 6 = Simplify.
– 9 = False
So (– 1, 6) is not a solution of 3x – y = 5.

11. Solving an Equation
If you know one coordinate in an ordered pair that is a solution for an equation, you can find the other coordinate through substitution and solving the resulting equation.

12. Solving an Equation Example:
Complete the ordered pair (4, __ ) so it is a solution of –2x + 4y = 4.
Let x = 4 in the equation and solve for y.
–2x + 4y = 4
–2(4) + 4y = Replace x with 4.
–8 + 4y = Simplify.
– y = Add 8 to both sides.
4y = 12 Simplify both sides.
y = Divide both sides by 4.
The completed ordered pair is (4, 3).

13. Solving an Equation Example:
Complete the ordered pair (__, – 2) so that it is a solution of 4x – y = 4.
Let y = – 2 in the equation and solve for x.
4x – y = 4
4x – (– 2) = Replace y with – 2.
4x + 2 = Simplify left side.
4x + 2 – 2 = 4 – Subtract 2 from both sides.
4x = Simplify both sides.
x = ½ Divide both sides by 4.
The completed ordered pair is (½, – 2).