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

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

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

Exhibit 5 Unemployment Rate Since 1900

Exhibits 6 & 7:Relating Distance Traveled to Hours Driven Hours Distance Driven Traveled Per Per Day Day (miles) a 1 50 b 2 100 c 3 150 d 4 200 e 5 250

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

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

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

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

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

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

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

Exhibit 10: Slopes at Different Points on a Curved Line y 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 10 20 30 40 x

Exhibit 11: Curves with Both Positive and Negative Ranges y 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

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 1 2 3 4 5 Hours driven per day