Econ 201/202
Review of Essential
Math and Graphing Skills
What do you need to know?
• Calculating and interpreting slopes of graphs
– Linear and non-linear functions
• Calculating and interpreting areas under a graph
– Geometric areas: triangles, rectangles
– More sophisticated – integrals (or summing
up)
• Systems of equations
– Interpreting the results
– Simultaneous equations and equilibrium
Slope of linear function
Demand Curve: Graphs of Two Variables (price and quantity)
FIGURE 1A-3
Plotting Price and Quantity
Points in a Graph
Appendix
Graphs of Two Variables
Slopes of Lines
Slope 
Change in value on the vertical axis

Δy
Change in value on the horizontal axis
Δx
($12  $14)
2

Rise
Run
FIGURE 1A-4
Calculating the
Slope of a Line
Slope 
Δ Price of pizza
Δ Quantity of pizza

(65  55)

10
  0.2
Appendix
Graphs of Two Variables
Deriving the slope from the equation
Y0 = a + bX0 at x,y = (55,14)
Y1 = a + bX1 or Y1 = Y0 +
FIGURE 1A-4
Calculating the
Slope of a Line
General form of a linear equation: Y = a + bX
Appendix
Graphs of Two Variables
Slopes of Lines in equation form
Change in value on the vertical axis
Δy
Rise
Slope 


Change in value on the horizontal axis
Δx
Run
FIGURE 1A-4
Calculating the
Slope of a Line
General form of a linear equation: Y = a + bX
Appendix
Graphs of Two Variables
Taking into Account More Than Two Variables on a Graph
FIGURE 1A-5
Showing Three
Variables on a Graph
Appendix
Graphs of Two Variables
Positive and Negative Relationships
FIGURE 1A-6
Graphing the Positive
Relationship between
Income and Consumption
Appendix
Graphs of Two Variables
Are Graphs of Economic Relationships Always Straight Lines?
The graphs of relationships between two economic
variables that we have drawn so far have been
straight lines.
The relationship between two variables is linear
when it can be represented by a straight line.
Few economic relationships are actually linear.
Appendix
Graphs of Two Variables
Slopes of Nonlinear Curves
FIGURE 1A-8
The Slope of a Nonlinear Curve
Appendix
Formulas
Formulas for the Areas of a Rectangle and a Triangle
Area of a rectangle  base x height
FIGURE 1A-9
Showing a Firm’s Total
Revenue on a Graph
Appendix
Formulas
Formulas for the Areas of a Rectangle and a Triangle
Area of a triangle  1/2 x base x height
FIGURE 1A-10
The Area of a Triangle
Appendix
Formulas
Formula for a Percentage Change
One important formula is the percentage change.
The percentage change is the change in some
economic variable, usually from one period to the next,
expressed as a percentage.
 GDP2004  GDP2003 

 x 100
GDP2003


Percentage change  (
Value in the second period - Value in the first period
) x 100
Value in the first period
Appendix
Formulas
Summary of Using Formulas
Whenever you must use a formula, you should follow
these steps:
1 Make sure you understand the economic
concept that the formula represents.
2 Make sure you are using the correct formula for
the problem you are solving.
3 Make sure that the number you calculate using
the formula is economically reasonable. For
example, if you are using a formula to calculate
a firm’s revenue and your answer is a negative
number, you know you made a mistake
somewhere.