Understanding Graphs CHAPTER 1 Appendix

Graph Picture showing how variables relate and 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 The value of variable x is measured along the horizontal axis and increases as you move to the right of the origin. The value of the variable 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.

Exhibits 6 & 7:Relating Distance Traveled to Hours Driven Hours Distance Driven Traveled Per Per Day Day (miles) a1 50 b2100 c3150 d4200 e5250

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 8a.) Positive relation

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

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

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

Exhibit 9: Slope Depends on the Unit of Measure $ Feet of copper tubing 1 1 Total Cost 0 Total Cost $ a) Slope = 1/1 = 1 b) Slope = 3/1 = 3 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 x b B B a A A Slope of curved line varies at different points along curve 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 Slope of the tangent at that point is the slope of the curve at that point 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  slope of -4

Exhibit 11: Curves with Both Positive and Negative Ranges y x b a 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.

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