The value of Y varies directly with the value of X. which function represents the relationship between X and Y if Y= 7/3 when X= 21?
A.) Y= 9x
B.) Y= 49x
C.) Y= 1/49x
D.) Y= 1/9x
When we say that "the value of Y varies directly with the value of X," we mean that Y = kX, where k is the constant of proportionality.
Given that Y = 7/3 when X = 21, we can determine the value of the constant k by substituting these values into the equation:
Y = kX
7/3 = k * 21
To find k, we divide both sides by 21:
(7/3) / 21 = k
k = (7/3) * (1/21)
Simplify the expression:
k = 7 / (3 * 21)
k = 7 / 63
k = 1/9
Therefore, the constant of proportionality k is 1/9, so the equation representing the relationship between X and Y is:
Y = (1/9)X
This corresponds to answer choice D:
D.) Y = 1/9X