# Illustrating Complex Relationships

In introductory courses such as chemistry, economics, political science, and psychology, you will often see a complex set of relations represented graphically. You will use graphs to make interpretations about what is happening as variables in a relationship change.

While the examples below are taken directly from different economics textbooks, they demonstrate the kinds of skills that you will be required to use in many non-math introductory courses.

### Example

 FIGURE 1: Changes in the supply of corn A change in one or more of the determinants of supply--resource prices, productive techniques, the prices of other goods, taxes and subsidies, price expectations, or the number of sellers in the market--will cause a change in supply. An increase in supply shifts the supply curve to the right as from S1 to S2. A decrease in supply is shown graphically as a shift of the curve to the left, as from S1 to S3. A change in the quantity supplied is caused by a change in the price of the product as is shown by a movement from one point to another--as from a to b--on a fixed supply curve. Adapted from: McConnell, C. R. & Brue, S. L. (1996) Macroeconomics: Principles, problems and policies (p. 47). New York: McGraw-Hill.

Figure 1 above shows changes in the supply of corn. In this graph you can see how the curve shifts as the supply either decreases or increases. In reading the legend of this graph you see that a number of variables can affect this shift.

### Example

 FIGURE 2 Market Equilibrium Comes at the Intersection of Supply and Demand Curves The market equilibrium price and quantity comes at the intersection of supply and demand curves. At a price of \$3 at point C, firms willingly supply what consumers willingly demand. When price is too low (say \$2), quantity demanded exceeds quantity supplied, shortages occur, and prices are driven up to equilibrium. What occurs at a price of \$4? Adapted from: Samuelson, P. A. & Stone, G. W. (1995) Microeconomics (p. 46). New York: McGraw-Hill.

Figure 2 shows how one can determine when market equilibrium occurs. This graph can be used to describe what happens when the quantity and price of a particular product changes. In your courses, you will need to be able to determine what are important points on a graph and how to identity them. This involves using the graph skills presented in this section.

The skills you will learn in this book are to:

• Describe how changing the y-intercept of a line affects the graph of a line.
• Describe how changing the slope of a line affects the graph of a line.
• Describe what has happened to an equation after a line on a graph has shifted.
• Identify the intersection of two lines on a graph.
• Describe what happens to the x and y coordinate values of intersecting lines after a shift in a line on the graph.
• Identify the Point of Tangency on a curve.
• Determine whether a line is a tangent line.
• Calculate the slope at a point on a curve.
• Determine whether the slope at a point on a curve is positive, negative, zero, or infinity.
• Identify maximum and minimum points on a curve.
• Determine whether a curve does or does not have maximum and minimum points.