Science 122 Lab 3 Graphs & Proportion # Laboratory # 2. LEARNING OUTCOMES

### After completing this exercise you should be able to do the following:

1. Define and explain the term "graph
2. Plot a proper graph of a linear relationship.
3. Label and name a properly drawn graph.
4. Plot a graph of a nonlinear relationship using a mathematical equation to obtain ordered pairs of numbers.
5. Distinguish between dependent and independent variables.
6. Define slope, determine the slope of a straight line, and equate the slope with the constant of proportion.
7. State the symbolic relationship for a straight line
8. State the general form of the relationship for a parabola.
9. Replot a parabola as a straight line.

# 3. EQUIPMENT AND SUPPLIES

• pencil, ruler, calculator, graph paper
• Drawing software may be used to draw graphs but it is not necessary
• Computer graphing software may be used but is not necessary*
• Chapter 5 in the Booth & Bloom text is be a useful reference

# 4. PROCEDURE 1: Circumference vs. Diameter

## Relationship 4.1

The number 'pi' ( ) is the ratio of the circumference of a circle to its diameter. It is the same for all circles because all circles are the same shape. The value of pi is approximately 3.14.

## Data Table 1.1

Diameter D)
(Independent)
Circumference (C)
(Dependent)
Ratio C/D

1 cm

2 cm

3 cm

4 cm

5 cm

6 cm

7 cm

D (cm)
(Independent)
C (cm)
(Dependent)
Ratio
C/D

# 5. PROCEDURE 2: Area vs. Radius

In this procedure you will produce a nonlinear graph where one variable is related to the second power of the other. The graph of this relationship will not be a straight line. This is known as a "direct square" proportion and the graph will curve upward.

# 6. PROCEDURE 3

## Data Table 2.2

radius (R) area/radius squared (A/R2) 1 2 3 4 5 6 7

# 7. QUESTIONS

### 7.1. Discuss the relationship between the following:

• constant of proportion
• ratio of dependent to independent variables
• slope of a straight line graph