LECTURE 2: MATH REVIEW

Graphs Economists use numbers to express many of the concepts in the field These concepts or variables are related to one another. For instance, when the price of tomatoes reduce, people buy more tomatoes One way of expressing the relationships among variables is by using graphs Three common graphs used for a single variable are: pie chart, bar graph and time-series graph

Math Review A graph is a two-dimensional representation of a set of numbers or data.

GRAPHS OF TWO VARIABLES: PLOTTING COORDINATES The Cartesian coordinate system is the most common method of showing the relationship between two variables. The horizontal line is the X-axis and the vertical line the Y-axis. The point at which the horizontal and vertical axes intersect is called the origin.

READING AND UNDERSTANDING GRAPHS The point at which the line intersects the Y-axis (point a) is called the Y-intercept. The Y-intercept, is the value of Y when X = 0

Reading and Understanding Graphs The slope of the line indicates whether the relationship between the variables is positive or negative. The slope of the line is computed as follows:

Reading and Understanding Graphs An upward-sloping line describes a positive relationship between X and Y. A downward-sloping line describes a negative relationship between X and Y.

Reading and Understanding Graphs This line slopes upward, indicating that there seems to be a positive relationship between income and spending. Points A and B, above the 45° line, show that consumption can be greater than income.

Reading and Understanding Graphs

Reading and Understanding Graphs

Tables and Graphs Advertising and Sales at Len & Harry’s

Straight-line Graphs A Graph of Advertising and Sales

Straight-line Graphs Slope of a straight line = Change in vertical variable / Change in horizontal variable and is constant at any point =

Curved Lines

Linear Equations Y = a+bX where a: vertical intercept b: slope Exercise: what is the linear equation for advertisement example? Y = 18+3X

Linear Equations Remember : Y= 18+3X For example, how much expenses are necessary to secure a sale $39,000? Y = $39 now $39 = 18 + 3X X = (39 – 18)/3 = 7

Linear Equations Straight Lines with Different Slopes and Vertical Intercepts

Linear Equations Straight Lines with Different Slopes and Vertical Intercepts

Straight Lines with Different Slopes and Vertical Intercepts

Line Shift-Shifts in the Graph of Advertising and Sales

Curve Shift-Shifts of Curved Lines

Shifts vs. Movements Along a Line Suppose Y is the dependent variable, which is measured on one of the axis. If the independent variable measured on the other axis changes, we move along the line. But if any other independent variable changes, the entire line shifts.