Mathematics
Grade 9
15 min
Celsius and Fahrenheit temperatures
Celsius and Fahrenheit temperatures
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1
Introduction & Learning Objectives
Learning Objectives
Convert temperatures between Celsius and Fahrenheit using the correct formulas.
Represent the relationship between Celsius and Fahrenheit as a linear function.
Solve for an unknown temperature by isolating a variable in the conversion formula.
Interpret the slope and y-intercept of the temperature conversion function in a real-world context.
Use function notation to evaluate temperature conversions.
Algebraically determine the temperature at which the Celsius and Fahrenheit scales are numerically equal.
Graph the linear function that relates the two temperature scales.
Ever see a weather report from the USA showing 86° and wonder what that feels like? Let's use math to decode temperatures from around the world! 🌍🌡️
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Key Concepts & Vocabulary
TermDefinitionExample
Celsius (°C)A unit of temperature on the metric scale, where water freezes at 0°C and boils at 100°C at standard atmospheric pressure.A pleasant spring day might be 20°C.
Fahrenheit (°F)A unit of temperature on the imperial scale, where water freezes at 32°F and boils at 212°F at standard atmospheric pressure.A hot summer day might be 86°F.
Linear FunctionA function whose graph is a straight line, typically written in the form y = mx + b. The relationship between Celsius and Fahrenheit is a perfect example of a linear function.The formula F = 1.8C + 32 is a linear function where F is the output (y) and C is the input (x).
Slope (m)The rate of change of a linear function, representing how much the dependent variable (y) changes for each one-unit increase in the indepe...
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Core Formulas
Celsius to Fahrenheit Conversion
F = \frac{9}{5}C + 32
Use this formula when you know the temperature in Celsius (C) and want to find the equivalent temperature in Fahrenheit (F). First, multiply the Celsius temperature by 9/5, then add 32.
Fahrenheit to Celsius Conversion
C = \frac{5}{9}(F - 32)
Use this formula when you know the temperature in Fahrenheit (F) and want to find the equivalent temperature in Celsius (C). First, subtract 32 from the Fahrenheit temperature, then multiply the result by 5/9.
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Challenging
The relationship between Fahrenheit and Celsius can be written as the linear equation 5F - 9C = 160. Using this equation, what is the temperature in Celsius when it is 86°F?
A.30°C
B.25°C
C.48°C
D.187°C
Challenging
At what temperature is the numerical value in degrees Fahrenheit exactly double the numerical value in degrees Celsius?
A.-24.6°C
B.160°C
C.80°C
D.-12.3°C
Challenging
If the function F(C) = (9/5)C + 32 is graphed on a coordinate plane, at what temperature value does its graph intersect the line y = x?
A.0
B.32
C.100
D.-40
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