Find a linear equation that expresses the relationship between the temperature in degrees Celsius C and degrees Fahrenheit F. Use the fact that water freezes at 0􏰆C (32􏰆F) and boils at 100􏰆C (212􏰆F). Use the equation to convert 72􏰆F to degrees Celsius.

To find the linear equation that expresses the relationship between degrees Celsius (\(C\)) and degrees Fahrenheit (\(F\)), we use the known points of water freezing and boiling:

1. Water freezes at \(0^\circ C\) and \(32^\circ F\).
2. Water boils at \(100^\circ C\) and \(212^\circ F\).

The equation of a line is typically in the form:

\[
F = mC + b
\]

Where:
- \(F\) is the temperature in Fahrenheit.
- \(C\) is the temperature in Celsius.
- \(m\) is the slope.
- \(b\) is the y-intercept (the value of \(F\) when \(C = 0\)).

### Step 1: Find the slope \(m\)

Using the two points \((0, 32)\) and \((100, 212)\), we can find the slope \(m\):

\[
m = \frac{F_2 - F_1}{C_2 - C_1} = \frac{212 - 32}{100 - 0} = \frac{180}{100} = 1.8
\]

### Step 2: Find the y-intercept \(b\)

Since we know that when \(C = 0\), \(F = 32\), the y-intercept \(b = 32\). So the equation becomes:

\[
F = 1.8C + 32
\]

### Step 3: Solve for \(C\)

To convert Fahrenheit to Celsius, we can rearrange the equation to solve for \(C\):

\[
C = \frac{F - 32}{1.8}
\]

### Step 4: Convert 72°F to Celsius

Using the equation \(C = \frac{F - 32}{1.8}\), we substitute \(F = 72\):

\[
C = \frac{72 - 32}{1.8} = \frac{40}{1.8} \approx 22.22^\circ C
\]

### Final Answer:
The temperature \(72^\circ F\) is approximately \(22.22^\circ C\).

Would you like further details or have any questions?

---

Here are 5 related questions:

1. How would the formula change if we were converting from Kelvin to Celsius?
2. What is the temperature in Fahrenheit for \(25^\circ C\)?
3. How do you derive the slope formula for a linear equation from two points?
4. What is the interpretation of the slope \(1.8\) in the context of this temperature conversion?
5. Can we use this linear equation for extreme temperatures, such as the temperature of the sun?

**Tip:** For quick temperature conversions between Celsius and Fahrenheit, remember the values 32°F (freezing) and 212°F (boiling) for reference points.

Find a linear equation that expresses the relationship between the temperature in degrees Celsius C and degrees Fahrenheit F. Use the fact that water freezes at 0°C (32°F) and boils at 100°C (212°F). Use the equation to convert 72°F to degrees Celsius.

Learn how to derive a linear equation that expresses the relationship between degrees Celsius and degrees Fahrenheit. This problem uses key temperature points, including water freezing at 0°C and boiling at 100°C. Also, see how to convert 72°F to Celsius using the derived formula. Suitable for students in Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation