SOLUTION: Water boils as C (degrees Celsius) which is F (degrees Fahrenheit) and freezes at C which is F. Let x denote the temperature of an object in F and y the temperature of the sam

Question 612782: Water boils as C (degrees Celsius) which is F (degrees Fahrenheit) and freezes at C which is F. Let x denote the temperature of an object in F and y the temperature of the same object in C.
(a) Express x in terms of y.
x(y)= F
(b) Express y in terms of x.
y(x)= C
(c) Use (b) to convert F into Celsius.
C
(d) Use (a) to convert your answer to (c) back into Fahrenheit.
F
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
Water boils at C (degrees Celsius) which is F (degrees Fahrenheit) and freezes at C which is F. Let x denote the temperature of an object in F and y the temperature of the same object in C.
So we have two points (A and B) of the line (the linear function) that relates y and x.
or
With the coordinates of two points, you can determine the slope and the equation of the line.

(a) Express x in terms of y.
x(y)= F
In the graph on the left, x increases by F-F=F (the vertical rise from A to B),
while y increases by C-C=C (the horizontal run from A to B).
So the slope is
With that slope, and the y-intercept from point A, we can write the slope-intercept form of the equation as
F

(b) Express y in terms of x.
y(x)= C
You start from scratch calculating the slope of the line, and then using that slope and point A to get the point slope form of the equation.
However, the easiest way to get the needed equation is to solve for y in the equation found in part (a).
--> --> -->
I would stop at C, because that is the equation I would use to do mental math conversions.
Transforming that into the slope-intercept form would give you a less user-friendly equation:
--> -->

(c) Use (b) to convert F into Celsius.
If I wanted to convert F into degrees Celsius to tell a very ill tourist his/her body temperature in familiar units, I would use the equation from part (b), to get
C (rounded from 40.55555....)

(d) Use (a) to convert your answer to (c) back into Fahrenheit.
F (rounded from 105.08)
Yes, rounding errors caused the final answer to be a tiny bit different from the F I started with.
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