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Answer :
Final answer:
To write degrees Celsius as a linear function of degrees Fahrenheit, use the freezing and boiling points of water in both scales to find the slope and y-intercept of the linear equation.
Explanation:
To write degrees Celsius as a linear function of degrees Fahrenheit, we need to find the equation of a line that relates the two variables. First, we know that the freezing point of water in degrees Celsius is 0 °C and in degrees Fahrenheit is 32 °F. We also know that the boiling point of water in degrees Celsius is 100 °C and in degrees Fahrenheit is 212 °F. We can use this information to find the slope and y-intercept of the linear equation.
To find the slope, we use the formula: slope = (change in y) / (change in x). In this case, the change in y is 100 - 0 = 100 and the change in x is 212 - 32 = 180. Therefore, the slope is 100 / 180 = 5 / 9.
The y-intercept is the value of y when x is 0. From the freezing point, we know that when x is 32, y is 0. Therefore, the y-intercept is 0 - (5/9)(32) = -17.78.
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Answer:
See below.
Step-by-step explanation:
a.
We need degrees C as a function of degrees F.
Just like when we have y as a function of x, we have (x, y) ordered pairs, here we will have (F, C) ordered pairs.
We are given two ordered pairs: (32, 0) and (212, 100).
We can find the slope of the line.
m = (100 - 0)/(212 - 32) = 100/180 = 5/9
y = mx + b
C = mF + b
C = (5/9)F + b
Use point (32, 0) for F and C to solve for b.
0 = (5/9)(32) + b
b = -(5/9)(32)
C = (5/9)F - 5/9(32)
C = (5/9)F - 160/9
b.
The slope is 5/9. The slope is the rate of change of degrees F to degrees C. For each change of 9 degrees F, the corresponding change in degrees C is 5.
c.
The y-intercept is -160/9.
It means that a temperature of 0 degrees F equals -160/9 degrees C.
