To determine the constant of proportionality for the proportional relationship given by the equation [tex]\( r = 355m \)[/tex], let's examine the equation step-by-step.
The given equation relates [tex]\( r \)[/tex] (the amount of rent) to [tex]\( m \)[/tex] (the number of months) by the following formula:
[tex]\[ r = 355m \][/tex]
In this type of linear proportional relationship, the constant of proportionality is the coefficient of [tex]\( m \)[/tex]. This coefficient is the constant value that [tex]\( r \)[/tex] is multiplied by to yield the amount of rent for any given number of months [tex]\( m \)[/tex].
From the equation, we can see that:
[tex]\[ r = 355 \times m \][/tex]
Comparing this with the general form of a proportional relationship [tex]\( r = k \times m \)[/tex], where [tex]\( k \)[/tex] is the constant of proportionality, it is clear that [tex]\( k = 355 \)[/tex].
Thus, the constant of proportionality [tex]\( k \)[/tex], which relates [tex]\( r \)[/tex] to [tex]\( m \)[/tex] in the given equation, is [tex]\( 355 \)[/tex].
Therefore, the correct answer is:
D. 355
