1. Understanding Graphs Origin Horizontal axis Vertical axis Graph
Functional relation
Dependent variable
Independent variable

2. Types of graphs
Scatter plot diagram: A graph of the value of one variable against the value of another variable
Time-series graph: A graph that measures time on the x-axis and the variable or variables of interest on the y-axis.
Cross-section graph: A graph that shows the values of a variable for different groups in the population at a point in time.

3. Scatter plot diagram
Source Money Magazine, Vol. 32, No. 1, January, 2004, pp

4. Time series graph
U.S. Unemployment

5. Bar chart using cross-sectional data
Age and salary of employees at Sasnak, Inc. (salary in thousands)
Bar chart using cross-sectional data

6. Basics of a graph Point a: - 5 units X - 15 units Y Point b:10 5 20 y
Vertical axis
Point b:
- 10 units X
- 5 units Y a b
Origin 20 15 10 5 x
Horizontal axis

7. Drawing Graphs Dependent variable Types of relations between variables
Depends on the independent variable
Types of relations between variables
Positive; direct
Negative; inverse
Independent; unrelated

8. Schedule and Graph relating distance traveled to hours driven
150
100 50
200
Distance traveled per day (miles)
250
Hours driven
per day
Distance traveled per day (miles) a b c d e 1 2 3 4 5 50
100
150
200
250 a b c d e 4 3 2 1
Hours driven per day 5
Points a through e depict different combinations of hours
driven per day and the corresponding distances traveled.
Connecting these points graphs a line.

9. Slopes of Straight Lines
Change in vertical variable
For a given increase in horizontal variable
Slope = Change in the vertical distance/ Increase in the horizontal distance
Slope of a straight line
The same value along the line

10. Alternative slopes for straight lines
(a) Positive relation
(b) Negative relation 10 15 20 y 10 3 20 y
Slope = 5/10 = 0.5 5
Slope = - 7 /10 = - 0.7 10 -7 10 x 20 10 x 20 10

11. Alternative slopes for straight lines
Exhibit 8 (c), (d)
Alternative slopes for straight lines
(c) No relation: zero slope
(d) No relation: infinite slope 10 15 20 y 10 20 y
Slope = 10 /0 = ∞ 10
Slope = 0/10 = 0 10 x 20 10 x 10

12. Slope, Units of Measurement, Marginal Analysis
Value of slope
Depends on units of measurement
Measures marginal effects

13. Slope depends on the unit of measure
(a) Measured in feet
(b) Measured in yards 5 $6
Total
cost 3 $6
Total
cost
Slope = 1/1 = 1
Slope = 3/1 = 3 1 3 1 1
Feet of copper tubing 6 5
Yards of copper tubing 2 1
Output is measured in feet of copper tubing.
Output is measured in yards.
The cost: $1 per foot.
Slope is different: copper tubing is measured using different units

14. The Slopes of Curved Lines
Differs along the curve
Slope of a curved line at one point
Slope of the tangent

15. Slope at different points on a curved line30 20 10 40 y
The slope of a curved line
varies from point to point. A
At point a, the slope of the curve
is equal to the slope of the tangent A. a
At point b, the slope of the curve
is equal to the slope of the tangent B. B b 40 30 20 10 x

16. Curves with both positive and negative slopes
Exhibit 11
Curves with both positive and negative slopes
Some curves have both positive
and negative slopes. y
The U-shaped curve has:
negative slope to the left of b
slope of 0 at point b
positive slope to the right of b. a b
The hill-shaped curve has:
positive slope to the left of a
slope of 0 at point a
negative slope to the right of a. x

17. Line Shifts Change assumptions Changed relationship between variables

18. Shift of line relating distance traveled to hours driven
Line T
hours driven/day and
distance traveled/day
average speed = 50 mph
150
100 50
200
Distance traveled per day (miles)
250 d T f T’
Line T’
hours driven/day and
distance traveled/day
average speed = 40 mph 4 3 2 1
Hours driven per day 5