The problem calls the equations functions, and they should be in function format:
S(M) = 0.60M + 15.75
and
I(M) = 0.16M + 3.90
where M is the number of miles driven and the Standard charge (S) is a function of the input value M and the Insurance charge (I) are a function also of the same input value M. The constants, coefficients, and function values all use dollars as their units.
Both of these are linear functions since the single input variable is not exponeniated and is multiplied by a constant and then a constant is added to it.
Because of this we can add and simplify these functions into one combined function:
C(M) = S(M) + I(M)
= ( 0.60M + 15.75 ) + ( 0.16M + 3.90 )
And using the aasociate property of addition:
= ( 0.60M + 0.16M ) + ( 15.75 + 3.90 )
Now, we apply the distributive property:
= ( 0.60 + 0.16 ) M + 19.65
Finally, simplifying:
= 0.76M + 19.65 = C(M)
By definition, C(M) is also a linear function. This can be verified by graphing it: a straight line results.
It is also important to know the arithmetic properties used so that you are performing valid operations when combining and/or simplifying equations. (In most instances, you will not be asked to list the properties used.)
