Chapter 3 Graphing

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

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.

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.

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.

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).

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.

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.

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) = – 4 Replace x with 3 and y with –2. 6 + (–10) = – 4 Simplify. – 4 = – 4 True So (3, –2) is a solution of 2x + 5y = – 4.

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 = 5 Replace x with – 1 and y with 6. – 3 – 6 = 5 Simplify. – 9 = 5 False So (– 1, 6) is not a solution of 3x – y = 5.

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.

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 = 4 Replace x with 4. –8 + 4y = 4 Simplify. –8 + 8 + 4y = 4 + 8 Add 8 to both sides. 4y = 12 Simplify both sides. y = 3 Divide both sides by 4. The completed ordered pair is (4, 3).

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) = 4 Replace y with – 2. 4x + 2 = 4 Simplify left side. 4x + 2 – 2 = 4 – 2 Subtract 2 from both sides. 4x = 2 Simplify both sides. x = ½ Divide both sides by 4. The completed ordered pair is (½, – 2).