Question

Which relationships have the same constant of proportionality between yyy and xxx as the equation y=\dfrac{1}{2}xy= 2 1 ​ xy, equals, start fraction, 1, divided by, 2, end fraction, x? Choose 3 answers: Choose 3 answers: (Choice A) A 6y=3x6y=3x6, y, equals, 3, x (Choice B) B (Choice C) C (Choice D) D xxx yyy 222 111 333 2.52.52, point, 5 444 333 (Choice E) E xxx yyy 444 222 555 2.52.52, point, 5 101010 555

Answer 1

The relationships with the same constant of proportionality as the equation y = ½x are found where y changes by ½ for each unit change in x. Choices A, D, and E all represent situations where this constant relationship is maintained.

Step-by-step explanation:

Two values or constants that are directly proportional indicate a relationship where a change in one leads to the equivalent change in the other, typically represented as y = kx where k is the constant of proportionality.

Given the equation y = ½x, we are looking for equations or sets of points where the relationship between y and x has the same constant of proportionality, meaning k will be ½. For Choice A, 6y = 3x can be rewritten as y = ½x by dividing both sides by 6, which shows that it has the same constant of proportionality. Choice B is incomplete and not given. In Choice D, the points (2, 1), (3, 1.5), and (4, 2) illustrate that for each unit increase in x, y increases by ½, which is also a direct proportionality with k = ½. Choice E presents points that also maintain this same ratio, making A, D, and E the correct answers with the same constant of proportionality as the given equation.