2. CHAPTER 6 Introduction to Graphing and Statistics Slide 2Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 6.1Tables and Pictographs 6.2Bar Graphs and Line Graphs 6.3Ordered Pairs and Equations in Two Variables 6.4Graphing Linear Equations 6.5Means, Medians, and Modes 6.6Predictions and Probability

3. OBJECTIVES 6.3 Ordered Pairs and Equations in Two Variables Slide 3Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. aPlot a point, given its coordinates. Find coordinates, given a point. bDetermine the quadrant in which a point lies. cDetermine whether an ordered pair is a solution of an equation with two variables.

4. 6.3 Ordered Pairs and Equations in Two Variables a Plot a point, given its coordinates. Find coordinates, given a point. Slide 4Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Bar graphs and line graphs are used to illustrate relationships between the items or quantities listed along the bottom and the side of the graph. The horizontal and vertical sides of a bar graph or line graph are often called the axes. By using two perpendicular number lines as axes, we can use points to represent solutions of certain equations.

5. 6.3 Ordered Pairs and Equations in Two Variables a Plot a point, given its coordinates. Find coordinates, given a point. Slide 5Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. When two number lines are used as axes, a grid can be formed. The grid provides a helpful way of locating any point on the plane. A point on a plane might be described as the intersection of a vertical line and a horizontal line.

6. 6.3 Ordered Pairs and Equations in Two Variables a Plot a point, given its coordinates. Find coordinates, given a point. Slide 6Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

7. 6.3 Ordered Pairs and Equations in Two Variables a Plot a point, given its coordinates. Find coordinates, given a point. Slide 7Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. The point 0, 0, where the axes cross each other, is called the origin. To graph, or plot, the point 3, 4, we can begin at the origin and move horizontally (along the first axis) to the number 3. From there, we move up 4 units vertically and make a “dot.” It is important to always make sure that the first coordinate matches the number that would be below (or above) the point on the horizontal axis. Similarly, the second coordinate should always match the number that would be to the left (or right) of the point on the vertical axis.

8. 6.3 Ordered Pairs and Equations in Two Variables a Plot a point, given its coordinates. Find coordinates, given a point. Slide 8Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

9. EXAMPLE 6.3 Ordered Pairs and Equations in Two Variables a Plot a point, given its coordinates. Find coordinates, given a point. 1 Slide 9Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Plot the points (–5, 2) and (2, –5). To plot (–5, 2), we locate –5 on the first, or horizontal, axis. From there we go up 2 units and make a dot. To plot (2, –5), we locate 2 on the first, or horizontal, axis. Then we go down 5 units and make a dot.

10. EXAMPLE 6.3 Ordered Pairs and Equations in Two Variables a Plot a point, given its coordinates. Find coordinates, given a point. 1 Slide 10Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

11. 6.3 Ordered Pairs and Equations in Two Variables a Plot a point, given its coordinates. Find coordinates, given a point. Slide 11Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. To determine the coordinates of a given point, we first look directly above or below the point to find the point’s horizontal coordinate. Then we look to the left (or right) of the point to identify the vertical coordinate.

12. EXAMPLE 6.3 Ordered Pairs and Equations in Two Variables a Plot a point, given its coordinates. Find coordinates, given a point. 2 Slide 12Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Determine the coordinates of points A, B, C, D, E, F, and G.

13. EXAMPLE 6.3 Ordered Pairs and Equations in Two Variables a Plot a point, given its coordinates. Find coordinates, given a point. 2 Slide 13Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. We look below point A to see that its first coordinate is 4. Looking to the left of point A, we find that its second coordinate is 3. Thus, the coordinates of point A are (4, 3). The coordinates of the other points are

14. 6.3 Ordered Pairs and Equations in Two Variables b Determine the quadrant in which a point lies. Slide 14Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. The axes divide the plane into four regions, or quadrants. For any point in region I (the first quadrant), both coordinates are positive. For any point in region II (the second quadrant), the first coordinate is negative and the second coordinate is positive. In region III (the third quadrant), both coordinates are negative. In region IV (the fourth quadrant), the first coordinate is positive and the second coordinate is negative.

15. 6.3 Ordered Pairs and Equations in Two Variables b Determine the quadrant in which a point lies. Slide 15Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. To determine whether an ordered pair is a solution of an equation, we normally substitute the first coordinate for the variable that comes first alphabetically and the second coordinate for the variable that is last alphabetically. The letters x and y are used most often.

16. EXAMPLE 6.3 Ordered Pairs and Equations in Two Variables c Determine whether an ordered pair is a solution of an equation with two variables. 3 Slide 16Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Determine whether the ordered pair (2, 1) is a solution of the equation 3x + 2y = 8.

17. 6.3 Ordered Pairs and Equations in Two Variables c Determine whether an ordered pair is a solution of an equation with two variables. Slide 17Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Unless stated otherwise, the coordinates of an ordered pair correspond alphabetically to the variables.