ERIE COMMUNITY COLLEGE
TITLE III
Linear Equations Project
Interdisciplinary Course Materials
Biology
Course: MT 007 Elementary Algebra I/ MT013 Elementary Algebra I and II
Course Outline Topics:
 Perform fundamental operations (addition, subtraction, multiplication, division) with real numbers.
 Determine the equation of a line using slope-intercept form.
 Read critically and think logically when solving application problems.
 Present organized written work.
Project Title: Temperature Conversion
Project description: In this project, the students will derive the equations to convert Celsius to Fahrenheit and
Fahrenheit to Celsius.
Author: Dianna Cichocki
Curriculum Expert: Rosanne Redlinski
Semester Created: Fall 2008
A.
Essential Question (What does this project attempt to answer?)
Can we derive the equations to convert Celsius to Fahrenheit and Fahrenheit to Celsius using our
knowledge of linear equations?
B.
Introduction
Temperature is commonly measured in degrees Fahrenheit (°F), degrees Celsius (°C), or Kelvin (K).
Americans generally refer to temperatures in degrees Fahrenheit. However, in the science laboratory
temperatures are reported in either degrees Celsius or Kelvin.
C.
Basic Directions
Students will use their knowledge of writing linear equations to derive the conversion equations.
D.
Things to Learn Before Starting the Project
Students should know the general form of a linear equation. Students should know how to calculate the
slope of a line between two points. Students should know how to write an equation given the slope and
a point on the line.
E.
The Project Assignment
In this project we will derive the formulas for converting from Celsius to Fahrenheit and Fahrenheit to
Celsius and then apply what we discover.
F.
Student Resources Basic Four Function Calculator.
H.
Grading Rubric
suggested - 20 points total – 2 points for #1-8 and 4 points for #9
Erie Community College
Title III Grant
Name _____________________________
Interdisciplinary Project (Math/Biology)
TEMPERATURE CONVERSION
Can we derive the equations to convert Celsius to Fahrenheit and Fahrenheit to Celsius using our
knowledge of linear equations?
To complete the above task we do need a bit of information:



Water boils at 212 °F and 100 °C
Water freezes at 32 °F and 0 °C
The general form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept.
A. Let’s begin by deriving the linear equation to convert Celsius to Fahrenheit:
1. In the space below use substitution to rewrite the general form of a linear equation (see above) in
terms of °C and °F instead of x and y, respectively. In this conversion, °C is the independent variable
(the measure we are converting from or the x-variable) and °F is the dependent variable (the measure we
are converting to or the y-variable).
2. In the above information we were given both the boiling point and freezing point of water in °F and °C.
We know that only 2 points are needed to determine the slope of a line. Knowing that °F is the yvariable and °C is the x-variable the boiling point of water is (C1,F1) or specifically (0, 32) and the
freezing point of water is (C2,F2) or specifically (100, 212). Using these two points find the slope (m)
of our line (leave your answer in simplest fraction form and show all work in the space below).
3. To find the y-intercept of the line (b) refer to your answer to #1. If you substitute in the value that you
determined for the slope and substitute either of the given points (choose either freezing or boiling) for
°C and °F you should only have one unknown variable (b). In the space below show your substitutions
and solve the equation for b (leave your answer in simplest fraction form).
4. Congratulations! You now have both components necessary to write the general form of the linear
equation necessary to convert Celsius to Fahrenheit (the slope and the y-intercept). In the space below
write the equation in terms of °C and °F.
Erie Community College
Title III Grant
B. Now let’s derive the linear equation to convert Fahrenheit to Celsius:
5. In the space below use substitution to rewrite the general form of a linear equation in terms of °F and °C
instead of x and y, respectively. In this conversion, °F is the independent variable (the measure we
are converting from or the x-variable) and °C is the dependent variable (the measure we are
converting to or the y-variable).
6. This time to determine the slope between the two points we need to remember that °F is the x-variable
and °C is the y-variable. Thus we have (F1,C1) or specifically (32, 0) and the freezing point of water is
(F2,C2) or specifically (212, 100). Using these two points find the slope (m) of our line (leave your
answer in simplest fraction form and show all work in the space below).
7. To find the y-intercept of the line (b) refer to your answer to #5. If you substitute in the value that you
determined for the slope and substitute either of the given points (choose either freezing or boiling) for
°F and °C you should only have one unknown variable (b). In the space below show your substitutions
and solve the equation for b (leave your answer in simplest fraction form).
8. Congratulations! You now have both components necessary to write the general form of the linear
equation necessary to convert Fahrenheit to Celsius (the slope and the y-intercept). In the space below
write the equation in terms of °F and °C.
C. The normal temperature of the human body is 98.6 °F. What is the corresponding
temperature in °C? (hint…use the equation derived in number 8 to help you determine the result) Show all
work in the space below.
Erie Community College
Title III Grant