Copyright © 2014, 2010, and 2006 Pearson Education, Inc. Chapter 3 Introduction to Graphing

3-2 Copyright © 2014, 2010, and 2006 Pearson Education, Inc. Reading Graphs, Plotting Points, and Scaling Graphs Problem Solving with Bar, Circle, and Line Graphs Points and Ordered Pairs Numbering the Axes Appropriately 3.1

3-3 Copyright © 2014, 2010, and 2006 Pearson Education, Inc. Bar Graphs A bar graph is a convenient way of showing comparisons. In every bar graph certain categories, such as level of education in the example, are paired with certain numbers.

3-4 Copyright © 2014, 2010, and 2006 Pearson Education, Inc. Example The bar graph shows the median weekly earnings for full-time wage and salary workers ages 25 and older. Estimate by how much the median weekly earnings of a high school graduate exceeds that of a person who did not earn a high school diploma.

3-5 Copyright © 2014, 2010, and 2006 Pearson Education, Inc. Example We locate “high school graduate” and go to the top of that bar. Then we move horizontally from the top of the bar to the vertical scale, which shows earnings. We read there about $600. Next repeat for “less than high school”, we read about $400. $600 – $400 = $200

3-6 Copyright © 2014, 2010, and 2006 Pearson Education, Inc. Points and Ordered Pairs To graph, or plot, points we use two perpendicular number lines called axes. The point at which the axes cross is called the origin. Arrows on the axes indicate the positive directions. Consider the pair (2, 3). The numbers in such a pair are called the coordinates. The first coordinate in this case is 2 and the second coordinate is 3.

3-7 Copyright © 2014, 2010, and 2006 Pearson Education, Inc. Points and Ordered Pairs continued To plot the point (2, 3) we start at the origin, move horizontally to the 2, move up vertically 3 units, and then make a “dot”. (2, 3)

3-8 Copyright © 2014, 2010, and 2006 Pearson Education, Inc. Example Plot the point (  4, 3). Solution Starting at the origin, we move 4 units in the negative horizontal direction (left). The second number, 3, is positive, so we move 3 units in the positive vertical direction (up). (–4, 3) 4 units left 3 units up

3-9 Copyright © 2014, 2010, and 2006 Pearson Education, Inc. Example A B C D E F G Find the coordinates of points A, B, C, D, E, F, and G. Solution A: (5, 3) B: (  2, 4) C: (  3,  4) D: (3,  2) E: (2, 3) F: (  3, 0) G: (0, 2)

3-10 Copyright © 2014, 2010, and 2006 Pearson Education, Inc. Quadrants The horizontal and vertical axes divide the plane into four regions, or quadrants.

3-11 Copyright © 2014, 2010, and 2006 Pearson Education, Inc. Numbering the Axes Appropriately Often it is necessary to graph a range of x-values and /or y-values that is too large to be displayed if each square of the grid is one unit wide and one unit high.

3-12 Copyright © 2014, 2010, and 2006 Pearson Education, Inc. Example Use a grid 10 square wide and 10 squares high to plot (  24, 460) and (38, 85) and (10,  170). Solution The x-values range from a low of  24 to a high of 38. The span is 38  (  24) = 62 units Because 62 is not a multiple of 10, we round up to the next multiple of 10, which is 70. Dividing 70 by 10 we would have a scale of 7 which is not convenient so we round up to 10.

3-13 Copyright © 2014, 2010, and 2006 Pearson Education, Inc. Example The y-values span from  170 to 460, the vertical squares must span from 460  (  170) = 630. For convenience, we round 630 up to 700, and then divide 700 by 10 = 70. Using 70 as the scale.

3-14 Copyright © 2014, 2010, and 2006 Pearson Education, Inc. Example Combine the work from the x and y-values to create the grid and plot the points. (  24, 460) and (38, 85) and (10,  170).