Question 998962
 The speed of sound in air changes with the temperature. 
 When the temperature T is 32 degrees Fahrenheit, the speed S of sound is 1087.5 feet per second.
 For each degree increase in temperature, the speed of sound increases by 1.1 feet per second. (Round your answers to two decimal places.)
:
(a) Explain why speed S is a linear function of temperature T.
Because S always increases by 1.1 ft/sec when T increases by .one degree,
 S has a constant rate of change and is a linear function of T.
Identify the slope of the function.
slope = rise/run, therefore 1.1/1, or just +1.1
.....
(b) Use a formula to express S as a linear function of T.
S = 1.1(t-32) + 1087.5
S = 1.1t - 35.2 + 1087.5
S = 1.1t + 1052.3 
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(c) Solve for T in the equation from part (b) to obtain a formula for temperature T as a linear function of speed S.
1.1t + 1052.3 = S
1.1t = S - 1052.3
t = {{{((S-1052.3))/1.1}}}
t = {{{S/1.1}}} - {{{1052.3/1.1}}}
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(d) Explain in practical terms the meaning of the slope of the function you 
found in part (c). Approx 1 ft/sec change indicates 1 degree of temperature change
The slope of T as a linear function of S is .91 , and this means that an increase in the speed of sound by 1 foot per second corresponds to an increase of ..one... degree in temperature.