Appendix to Chapter 1
Applying Graphs to Economics
APPENDIX SUMMARY
In economics, graphs are used as visual aids to illustrate relationships between economic
variables. If a relationship exists between two variables, then the relationship is either direct (also
known as a positive relationship) or inverse (also known as a negative relationship).
A direct relationship between two variables means that as one variable increases (the
independent variable) this causes the other variable (the dependent variable) to also increase in
value; and vice versa. A direct relationship is illustrated graphically as an upward sloping, or
positively sloped line or curve.
An inverse relationship between two variables means that as one variable increases (the
independent variable) this causes the other variable (the dependent variable) to decrease in value;
and vice versa. An inverse relationship is illustrated graphically as a downward sloping, or
negatively sloped line or curve.
An independent relationship means there is no relationship between two variables. This is
expressed graphically as a horizontal line.
A shift in a curve (or line) occurs when the ceteris paribus assumption is relaxed and a third
variable not on either axis of the graph is allowed to change.
NEW CONCEPTS INTRODUCED
direct relationship slope
inverse relationship independent relationship
,LEARNING OBJECTIVES
After completing this appendix, you should be able to:
1. Explain a direct relationship between two variables.
2. Explain an inverse relationship between two variables.
3. Understand the slope of a line.
4. Explain an independent relationship between two variables.
5. Explain a three-variable relationship.
APPENDIX TO CHAPTER 1 OUTLINE
A-1 A Direct Relationship
Exhibit A-1 "A Direct Relationship between Variables"
A-2 An Inverse Relationship
Exhibit A-2 "An Inverse Relationship between Variables"
A-3 The Slope of a Straight Line
Exhibit A-3 "An Independent Relationship between Variables"
Exhibit A-4 "The Slope of an Upward-Sloping Curve"
Exhibit A-5 "The Slope of a Downward-Sloping Curve"
,A-4 A Three-Variable Relationship in One Graph
Exhibit A-6 "Changes in Price, Quantity, and Income in Two Dimensions"
A-5 A Helpful Study Hint Using Graphs
Summary of Conclusion Statements
a. A shift in a curve occurs only when the ceteris paribus assumption is relaxed and a third
variable not on either axis of the graph is allowed to change.
HINTS FOR EFFECTIVE TEACHING
1. Stress the limitations of theory---especially association versus causation. Just because two
things happen to occur together doesn't mean one necessarily causes the other. For example,
the rooster may think his crowing is causing the sun to rise but we know better.
2. Providing a solid understanding of graphs will avoid many problems later. Point out that the
dependent variable goes on the "Y" or vertical axis. The independent variable goes on the "X" or
horizontal axis. A direct (also known as a positive) relationship is always expressed as a
positively sloped line or curve. An inverse (negative) relationship always has a negative slope.
Take several examples from outside the world of economics and ask students how they would
be graphed (see "Critical Thinking/Group Discussion Question" # 6 below).
3. Remind students that we often use graphs as a visual aid to illustrate relationships. Graphs are
often preferred to simply stating what a relationship is or expressing that relationship in terms
of a numerical table or a mathematical equation. Most people prefer graphs over the
alternative mathematical expression! So, maybe graphs aren’t so bad after all!
, 4. Explain that the general form for the equation of a straight line is: y = mx + b where “m” is the
slope and “b” is the y-intercept (and “y” is the dependent variable and “x” is the independent
variable). At a glance we can tell what the relationship is by simply looking at the sign of the
slope (a positive value implies a direct or positive relationship and a negative value implies a
negative or inverse relationship). Moreover, the absolute value of the slope indicates the extent
to which the variable y changes for every one unit change in x. Also note that changes in the
value of “b” indicates a shift of the line. This can come in handy later when discussing demand
and supply curves.
CRITICAL THINKING /GROUP DISCUSSION QUESTIONS
1. What is the relationship between the annual sale of umbrellas and the annual amount of rainfall
received in inches. How would this relationship be graphed?
Direct relationship. The line or curve slopes upward (positive slope). The variable "annual sale
of umbrellas" would be placed on the vertical axis (or "Y" axis) because it is the dependent
variable while the variable "annual amount of rainfall received in inches" would be placed on
the horizontal (or "X" axis) because it is the independent variable.
2. What is the relationship between a student's grade point average and the number of hours
spent studying per week. How would this relationship be graphed?
Direct relationship. The line or curve slopes upward (positive slope). The variable "grade point
average" would be placed on the vertical axis (or "Y" axis) because it is the dependent variable
while the variable "hours spent studying per week" would be placed on the horizontal (or "X"
axis) because it is the independent variable.
3. What is the relationship between tuition and student enrollment at a university. How would
this relationship be graphed?
Inverse relationship. The line or curve slopes downward (negative slope). The variable
"student enrollment" would be placed on the vertical axis (or "Y" axis) because it is the
Applying Graphs to Economics
APPENDIX SUMMARY
In economics, graphs are used as visual aids to illustrate relationships between economic
variables. If a relationship exists between two variables, then the relationship is either direct (also
known as a positive relationship) or inverse (also known as a negative relationship).
A direct relationship between two variables means that as one variable increases (the
independent variable) this causes the other variable (the dependent variable) to also increase in
value; and vice versa. A direct relationship is illustrated graphically as an upward sloping, or
positively sloped line or curve.
An inverse relationship between two variables means that as one variable increases (the
independent variable) this causes the other variable (the dependent variable) to decrease in value;
and vice versa. An inverse relationship is illustrated graphically as a downward sloping, or
negatively sloped line or curve.
An independent relationship means there is no relationship between two variables. This is
expressed graphically as a horizontal line.
A shift in a curve (or line) occurs when the ceteris paribus assumption is relaxed and a third
variable not on either axis of the graph is allowed to change.
NEW CONCEPTS INTRODUCED
direct relationship slope
inverse relationship independent relationship
,LEARNING OBJECTIVES
After completing this appendix, you should be able to:
1. Explain a direct relationship between two variables.
2. Explain an inverse relationship between two variables.
3. Understand the slope of a line.
4. Explain an independent relationship between two variables.
5. Explain a three-variable relationship.
APPENDIX TO CHAPTER 1 OUTLINE
A-1 A Direct Relationship
Exhibit A-1 "A Direct Relationship between Variables"
A-2 An Inverse Relationship
Exhibit A-2 "An Inverse Relationship between Variables"
A-3 The Slope of a Straight Line
Exhibit A-3 "An Independent Relationship between Variables"
Exhibit A-4 "The Slope of an Upward-Sloping Curve"
Exhibit A-5 "The Slope of a Downward-Sloping Curve"
,A-4 A Three-Variable Relationship in One Graph
Exhibit A-6 "Changes in Price, Quantity, and Income in Two Dimensions"
A-5 A Helpful Study Hint Using Graphs
Summary of Conclusion Statements
a. A shift in a curve occurs only when the ceteris paribus assumption is relaxed and a third
variable not on either axis of the graph is allowed to change.
HINTS FOR EFFECTIVE TEACHING
1. Stress the limitations of theory---especially association versus causation. Just because two
things happen to occur together doesn't mean one necessarily causes the other. For example,
the rooster may think his crowing is causing the sun to rise but we know better.
2. Providing a solid understanding of graphs will avoid many problems later. Point out that the
dependent variable goes on the "Y" or vertical axis. The independent variable goes on the "X" or
horizontal axis. A direct (also known as a positive) relationship is always expressed as a
positively sloped line or curve. An inverse (negative) relationship always has a negative slope.
Take several examples from outside the world of economics and ask students how they would
be graphed (see "Critical Thinking/Group Discussion Question" # 6 below).
3. Remind students that we often use graphs as a visual aid to illustrate relationships. Graphs are
often preferred to simply stating what a relationship is or expressing that relationship in terms
of a numerical table or a mathematical equation. Most people prefer graphs over the
alternative mathematical expression! So, maybe graphs aren’t so bad after all!
, 4. Explain that the general form for the equation of a straight line is: y = mx + b where “m” is the
slope and “b” is the y-intercept (and “y” is the dependent variable and “x” is the independent
variable). At a glance we can tell what the relationship is by simply looking at the sign of the
slope (a positive value implies a direct or positive relationship and a negative value implies a
negative or inverse relationship). Moreover, the absolute value of the slope indicates the extent
to which the variable y changes for every one unit change in x. Also note that changes in the
value of “b” indicates a shift of the line. This can come in handy later when discussing demand
and supply curves.
CRITICAL THINKING /GROUP DISCUSSION QUESTIONS
1. What is the relationship between the annual sale of umbrellas and the annual amount of rainfall
received in inches. How would this relationship be graphed?
Direct relationship. The line or curve slopes upward (positive slope). The variable "annual sale
of umbrellas" would be placed on the vertical axis (or "Y" axis) because it is the dependent
variable while the variable "annual amount of rainfall received in inches" would be placed on
the horizontal (or "X" axis) because it is the independent variable.
2. What is the relationship between a student's grade point average and the number of hours
spent studying per week. How would this relationship be graphed?
Direct relationship. The line or curve slopes upward (positive slope). The variable "grade point
average" would be placed on the vertical axis (or "Y" axis) because it is the dependent variable
while the variable "hours spent studying per week" would be placed on the horizontal (or "X"
axis) because it is the independent variable.
3. What is the relationship between tuition and student enrollment at a university. How would
this relationship be graphed?
Inverse relationship. The line or curve slopes downward (negative slope). The variable
"student enrollment" would be placed on the vertical axis (or "Y" axis) because it is the
