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.
