 Graphs’ purposes: ◦ Visually express ideas that might be less clear if described with equations or words Q(p) = a + b*p ◦ Powerful way of finding and interpreting patterns  Increasing / decreasing over time? 1

 Graphs of two variables: the coordinate system ◦ Display two variables on a single graph ◦ Scatterplot ◦ Ordered pairs of points  x-coordinate  Horizontal location  y-coordinate  Vertical location © 2011 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password- protected website for classroom use.2

 climb.html?ref=politics climb.html?ref=politics

 A graph is a two-dimensional representation of a set of numbers, or data.  A time series graph shows how a single measure or variable changes over time. How to Read and Understand Graphs CHAPTER 1 APPENDIX Time Series Graphs

TABLE 1A.1 Total Disposable Personal Income in the United States, 1975–2012 (in billions of dollars) Year Total Disposable Personal Income Year Total Disposable Personal Income , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , ,930.6  FIGURE 1A.1 Total Disposable Personal Income in the United States: 1975–2012 (in billions of dollars)

Graphing Two Variables X-axis The horizontal line against which a variable is plotted. Y-axis The vertical line against which a variable is plotted. origin The point at which the horizontal and vertical axes intersect. Y-intercept The point at which a graph intersects the Y-axis. X-intercept The point at which a graph intersects the X-axis.

7use. Using the Coordinate System Grade point average is measured on the vertical axis and study time on the horizontal axis. Albert E., Alfred E., and their classmates are represented by various points. We can see from the graph that students who study more tend to get higher grades.

A graph is a simple two-dimensional geometric representation of data. This graph displays the data from Table 1A.2. Along the horizontal scale (X-axis), we measure household income. Along the vertical scale (Y-axis), we measure household consumption. Note: At point A, consumption equals $22,304 and income equals $10,263. At point B, consumption equals $31,751 and income equals $27,442. TABLE 1A.2 Consumption Expenditures and Income, 2008 Average Income Before Taxes Average Consumption Expenditures Bottom fifth 2nd fifth 3rd fifth 4th fifth Top fifth $ 10,263 27,442 47,196 74, ,652 $ 22,304 31,751 42,659 58,632 97,003  FIGURE 1A.2 Household Consumption and Income Plotting Income and Consumption Data for Households

 Curves in the coordinate system  Negatively related variables ◦ The two variables move in opposite direction ◦ Downward sloping curve  Positively related variables ◦ The two variables move in the same direction ◦ Upward sloping curve  Movement along a curve  Shifts in a curve © 2011 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password- protected website for classroom use.9

Slope slope A measurement that indicates whether the relationship between variables is positive or negative and how much of a response there is in Y (the variable on the vertical axis) when X (the variable on the horizontal axis) changes.

 FIGURE 1A.3 A Curve with (a) Positive Slope and (b) Negative Slope A positive slope indicates that increases in X are associated with increases in Y and that decreases in X are associated with decreases in Y. A negative slope indicates the opposite — when X increases, Y decreases; and when X decreases, Y increases.

 FIGURE 1A.4 Changing Slopes Along Curves

13. Demand Curve The line D 1 shows how Emma’s purchases of novels depend on the price of novels when her income is held constant. Because the price and the quantity demanded are negatively related, the demand curve slopes downward. Quantity of novels purchased Price of Novels $11 Demand, D 1 (25, $5) (21, $6) (17, $7) (13, $8) (9, $9) (5, $10)

14 Shifting Demand Curves The location of Emma’s demand curve for novels depends on how much income she earns. The more she earns, the more novels she will purchase at any given price, and the farther to the right her demand curve will lie. Curve D 1 represents Emma’s original demand curve when her income is $30,000 per year. If her income rises to $40,000 per year, her demand curve shifts to D 2. If her income falls to $20,000 per year, her demand curve shifts to D 3. Quantity of novels purchased Price of Novels $11 D 3 (income= $20,000) (10, $8) D 2 (income= $40,000) (16, $8) D 1 (income= $30,000) (13, $8) 1316 When income increases, the demand curve shifts to the right. When income decreases, the demand curve shifts to the left.

 Slope ◦ Ratio of the vertical distance covered ◦ To the horizontal distance covered ◦ As we move along the line  Δ (delta) = change in a variable  The “rise” (change in y) divided by the “run” (change in x)..15

 Slope ◦ Fairly flat upward-sloping line  Slope = small positive number ◦ Steep upward-sloping line  Slope = large positive number ◦ Downward sloping line  Slope = negative number ◦ Horizontal line  Slope = zero ◦ Vertical line  Infinite slope. 16

17 Calculating the Slope of a Line To calculate the slope of the demand curve, we can look at the changes in the x- and y-coordinates as we move from the point (21 novels, $6) to the point (13 novels, $8). The slope of the line is the ratio of the change in the y-coordinate (–2) to the change in the x-coordinate (+8), which equals –1⁄4. Quantity of novels purchased Price of Novels $11 Demand, D 1 (21, $6) (13, $8) = =8