Question

a. write degrees celsius as a linear function of degrees fahrenheit (1 point).
b. what is the slope of your linear equation? what does it mean? (1 point)
c. what is the y - intercept and what does it mean? (1 point)

Explanation:

Step1: Recall conversion formula

The conversion formula from Fahrenheit ($F$) to Celsius ($C$) is $C=\frac{5}{9}(F - 32)$. This is a linear - function of the form $y = mx + b$, where $y = C$, $x = F$, $m=\frac{5}{9}$, and $b=-\frac{160}{9}$.

Step2: Identify the slope

The slope $m$ of the linear equation $C=\frac{5}{9}(F - 32)=\frac{5}{9}F-\frac{160}{9}$ is $\frac{5}{9}$. It means that for every 1 - degree increase in Fahrenheit, the Celsius temperature increases by $\frac{5}{9}$ degrees.

Step3: Identify the y - intercept

The y - intercept $b$ of the linear equation $C=\frac{5}{9}F-\frac{160}{9}$ is $-\frac{160}{9}$. When $F = 0$ (i.e., 0 degrees Fahrenheit), the Celsius temperature is $-\frac{160}{9}\approx - 17.78$ degrees Celsius.

Answer:

a. $C=\frac{5}{9}(F - 32)=\frac{5}{9}F-\frac{160}{9}$
b. Slope: $\frac{5}{9}$. It means for every 1 - degree increase in Fahrenheit, Celsius increases by $\frac{5}{9}$ degrees.
c. y - intercept: $-\frac{160}{9}$. It means when it is 0 degrees Fahrenheit, it is $-\frac{160}{9}$ degrees Celsius.