To determine which equation has a constant of proportionality of 5, we need to recall the form of a proportional relationship, which is given by
[tex]\[ y = kx \][/tex]
where [tex]\( k \)[/tex] is the constant of proportionality.
Let’s examine each option:
- A. [tex]\( y = 5 - x \)[/tex]: This equation is not in the form [tex]\( y = kx \)[/tex]; it includes a subtraction operation and therefore does not represent a proportional relationship with a constant of 5.
- C. [tex]\( y = 10x \)[/tex]: This equation is in the proportional form [tex]\( y = kx \)[/tex], but here the constant of proportionality [tex]\( k \)[/tex] is 10, not 5.
- B. [tex]\( y = x + 5 \)[/tex]: This equation includes an addition operation and is not in the proportional form [tex]\( y = kx \)[/tex]. Therefore, it does not have a constant of proportionality.
- D. [tex]\( y = 5x \)[/tex]: This equation is in the form [tex]\( y = kx \)[/tex], with the constant of proportionality [tex]\( k \)[/tex] being 5.
Thus, out of the given options, the equation that has a constant of proportionality of 5 is:
D. [tex]\( y = 5x \)[/tex]
