Science 122Laboratory 
Introduction 
Outcomes 
Supplies 
Procedure 1 
Procedure 2 
Procedure 3 
Questions 
Key Points to Note 
The constant of proportion of a linear relationship is the same number as the slope of the graph that plots the relationship. 
Definition: constant of proportion  the constant value of the ratio of two proportional quantities x and y; usually written y/x = k or y = kx, where k is the constant of proportion. 
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. C= x Dwhere C = the circumference,D = the diameter,= 3.14 
1. Round off the calculated circumferences to two decimal places.
2. Complete the ratio (C/D) column by dividing the number in the circumference (C) column by the number in the same row of the diameter (D) column.
Diameter D) (Independent) 
Circumference (C) (Dependent) 
Ratio C/D 

1 cm 

2 cm 

3 cm 

4 cm 

5 cm 

6 cm 

7 cm 
Point of interest
A linear relationship (also called a direct proportion) has the general form y = mx+b, where
"y" is the dependent variable
"m" is the slope of the graph
"x" is the independent variable
"b" is the intercept (where the line crosses the yaxis; this number is not significant for this exercise)
Measure the circles! Do not use the formula to calculate the circumference. 
D (cm) (Independent) 
C (cm) (Dependent) 
Ratio C/D 
















Data 1.2 will probably not fall on a straight line because these are 'real' circles, not 'perfect' circles, and there is no 'perfect' measurement. Measurements always contain errors and we will learn more about measurement and errors in lab 5.
If the table 1.2 data does not fit a straight line, use a ruler to draw a straight line that comes closest to all of the points. This is known as a 'best fit' line, or 'regression line'.Here is information about how to draw the best fit line.
Excel or other spreadsheet programs will draw the best fit line ('trendline') and calculate the slope. See the links above for tutorials on using Excel to draw graphs.
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.
RELATIONSHIP 5.1 
Area = x (radius) squared OR A = R^{2}the area A is in square centimeters (cm^{2})the radius R in centimeters= 3.14. 
1. Round off the calculated circumferences to two decimal places.
2. Complete the ratio (A/R) column by dividing the number in the Area (A) column by the number in the same row of the radius (R) column.
radius (R)  radius squared (R^{2})  area (A) 
Area/radius 

1 

2 

3 

4 

5 

6 

7 
radius (R)  radius squared (R^{2})  area (A) 
area/radius squared 

1 

2 

3 

4 

5 

6 

7 
Point of interest 
Data from an experiment in the laboratory may yield a curve whose relationship is not obvious. The type of relationship can often be determined when the data are replotted in order to obtain a straight line. 