1. Chapter 1 Appendix
Understanding Graphs
© 2006 Thomson/South-Western

2. Graph Shows how variables relate
Conveys information in a compact and efficient way
Functional relation exists between two variables when the value of one variable depends on another
The value of the dependent variable depends on the value of the independent variable

3. Exhibit 4: Basics of a Graph
Value of x is measured along the horizontal axis and increases as you move to the right of the origin.
The value of y is measured along the vertical axis and increases as you move upward.
Any point on a graph represents a combination of particular values of two variables.
For example, point a represents the combination of 5 units of variable x and 15 units of variable y, while point b represents 10 units of x and 5 units of y

4. Exhibit 5 Unemployment Rate Since 1900

5. Exhibits 6 & 7:Relating Distance Traveled to Hours Driven
Hours Distance
Driven Traveled
Per Per Day
Day (miles) a
b 2 100
c 3 150
d 4 200
e 5 250

6. Slopes of Straight Lines
Indicates how much the vertical variable changes for a given change in the horizontal variable
Vertical Change divided by the horizontal Change
Slope = Change in the vertical distance / change in the horizontal distance

7. Exhibit 8: Alternative Slopes for Straight Lines
8(a) Positive relation

8. Exhibit 8: Alternative Slopes for Straight Lines
8(b) Negative relation

9. Exhibit 8: Alternative Slopes for Straight Lines
8(c) No relation: zero slope

10. Exhibit 8: Alternative Slopes for Straight Lines
8(d) No relation: infinite slope

11. Exhibit 9: Slope Depends on the Unit of Measure
a) Slope = 1/1 = 1
b) Slope = 3/1 = 3 $6 $6
Total Cost
Total Cost 1 5 3 1 3 1
5 6
1 2
Feet of copper tubing
Yards of copper tubing

12. Slope and Marginal Analysis
Economic analysis usually involves marginal analysis
The slope is a convenient device for measuring marginal effects because it reflects the change in one variable – the effect -- compared to the change in some other variable – the cause
Slope of straight line is the same everywhere along the line

13. Exhibit 10: Slopes at Different Points on a Curved Liney
With line AA tangent to the curve at point a, the horizontal value increases from 0 to 10 while the vertical value falls from 40 to 0
The vertical change divided by the horizontal change equals –40/10, or –4, which is the slope of the curve at point a. This slope is negative because the curve slopes downward at that point.
Draw a straight line that just
touches the curve at a point but does not cut or cross the curve – tangent to the curve at that point A 40 30 20 a b B 10 A x

14. Exhibit 11: Curves with Both Positive and Negative Rangesy
The hill-shaped curve begins with a positive slope to the left of point a, a slope of 0 at point a, and a negative slope to the right of point a.
The U-shaped curve begins with a negative slope, has a slope of 0 at point b, and a positive slope after point b. a b x

15. Exhibit 12: Shift in Curve Relating Distance Traveled to Hours Driven) s e l i T m (
250 f T' y a d d r
200
A change in the assumption about average speed changes the relationship between the two variables. e p d e
150 l e v a r
100 t e c n 50 a t s i D
Hours driven per day