To determine the correct equation that represents the relationship between [tex]\( x \)[/tex] and [tex]\( y \)[/tex], we need to translate the given condition into an algebraic expression.
The problem states that the number [tex]\( y \)[/tex] is [tex]\( 84 \)[/tex] less than the number [tex]\( x \)[/tex]. This means that if we start with the number [tex]\( x \)[/tex] and subtract [tex]\( 84 \)[/tex], we will get [tex]\( y \)[/tex].
Let's set up this relationship:
[tex]\[ y = x - 84 \][/tex]
This equation directly shows that [tex]\( y \)[/tex] is 84 less than [tex]\( x \)[/tex]. Now, let's compare this with the given options:
(A) [tex]\( y = x + 84 \)[/tex] : This equation suggests that [tex]\( y \)[/tex] is 84 more than [tex]\( x \)[/tex], which does not match the given relationship.
(B) [tex]\( y = \frac{1}{84}x \)[/tex] : This equation suggests a proportional relationship, which does not fit the description provided.
(C) [tex]\( y = 84x \)[/tex] : This equation implies multiplication, which again does not describe the relationship given in the problem.
(D) [tex]\( y = x - 84 \)[/tex] : This equation correctly represents that [tex]\( y \)[/tex] is 84 less than [tex]\( x \)[/tex].
Hence, the correct equation that represents the relationship between [tex]\( x \)[/tex] and [tex]\( y \)[/tex] is:
[tex]\[ \boxed{y = x - 84} \][/tex]
