Final answer:
The equation that represents direct proportionality between y and x, given y=7 when x=14, is D) y = (1/2)x. This equation aligns with the proportionality constant k, which in this case is 1/2, and satisfies the given values of y and x.
Step-by-step explanation:
The equation that best represents direct proportionality between y and x, given that when y is 7 and x is 14, is found by first identifying the proportionality constant (k). Each of the options provided can be examined by substituting the given values of y and x. The correct proportionality equation will satisfy the condition y = kx, where k is a constant. Substituting the given values into each option:
- A) y = 7(x) does not yield y = 7 when x = 14.
- B) y = x/7 gives y = 14/7 = 2, which is not equal to 7.
- C) y = 2(x) gives y = 2(14) = 28, which is also incorrect.
- D) y = (1/2)(x) gives y = (1/2)(14) = 7, which is the correct answer and shows that y is directly proportional to x with k = 1/2.
Therefore, option D) y = (1/2)x is the equation that represents the direct proportion between y and x, satisfying the given values.