Questions: The relationship between Celsius temperature, C, and Fahrenheit temperature, F, can be described by a linear equation in the form F=mC+b. The graph of this equation contains the point (100,212) : Water boils at 100°C or 212°F, The line also contains the point (0,32) : Water freezes at 0°C or 32°F. Write the linear equation expressing Fahrenheit temperature in terms of Celsius temperature. F ≈

The relationship between Celsius temperature, C, and Fahrenheit temperature, F, can be described by a linear equation in the form F=mC+b. The graph of this equation contains the point (100,212) : Water boils at 100°C or 212°F, The line also contains the point (0,32) : Water freezes at 0°C or 32°F. Write the linear equation expressing Fahrenheit temperature in terms of Celsius temperature.

F ≈

Transcript text: Points: 0 of 1 The relationship between Celsius temperature, C, and Fahrenheit temperature, F, can be described by a linear equation in the form $\mathrm{F}=\mathrm{mC}+\mathrm{b}$. The graph of this equation contains the point $(100,212)$ : Water bolls at $100^{\circ} \mathrm{C}$ or $212^{\circ} \mathrm{F}$, The line also contains the point $(0,32)$ : Water freezes at $0^{\circ} \mathrm{C}$ or $32^{\circ} \mathrm{F}$. Write the linear equation expressing Fahrenheit temperature in terms of Celsius temperature. \[ \mathrm{F} \approx \square \]

Solution

Solution Steps

To find the linear equation expressing Fahrenheit temperature in terms of Celsius temperature, we need to determine the slope (m) and the y-intercept (b) of the line that passes through the given points (0, 32) and (100, 212). The slope can be calculated using the formula $ m = \frac{y_2 - y_1}{x_2 - x_1} $. Once we have the slope, we can use one of the points to solve for the y-intercept using the equation $ F = mC + b $.

Step 1: Determine the Slope

To find the slope $ m $ of the line that passes through the points $ (0, 32) $ and $ (100, 212) $, we use the formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{212 - 32}{100 - 0} = \frac{180}{100} = 1.8 \]

Step 2: Calculate the Y-Intercept

Next, we calculate the y-intercept $ b $ using the point $ (0, 32) $: \[ b = y - m \cdot x = 32 - 1.8 \cdot 0 = 32 \]

Step 3: Write the Linear Equation

Now that we have both the slope and the y-intercept, we can express the linear equation relating Fahrenheit temperature $ F $ to Celsius temperature $ C $: \[ F = 1.8C + 32 \]