Question

Which relation is a direct variation that contains the ordered pair (2, 7)?

y = 4x - 1
y = 7/x
y = 2/7x
y = 7/2x

Answer 1

The equation that represents a direct variation and contains the ordered pair (2, 7) is y = 7/2x. This equation is in the form y = kx, which indicates direct proportionality and passes through the origin, characterizing it as a direct variation relation.

Step-by-step explanation:

The student asks which relation is a direct variation that contains the ordered pair (2, 7). The equation representing directly proportional variables is of the form y = kx, where k is the proportionality constant and the line will pass through the origin.

Testing the ordered pair (2, 7) in the given equations:

1. y = 4x - 1: For x = 2, y = 4(2) - 1 = 8 - 1 = 7. However, this equation has a y-intercept of -1, not 0, so it's not a direct variation.
2. y = 7/x: For x = 2, y = 7/2, which is not 7, so this equation is not a direct variation containing the pair (2, 7).
3. y = 2/7x: For x = 2, y = (2/7)(2) = 4/7, which is not 7, so this equation is not a direct variation containing the pair (2, 7).
4. y = 7/2x: For x = 2, y = (7/2)(2) = 7. This equation also has the form of y = kx where k = 7/2 and passes through the origin, so it is a direct variation including the pair (2, 7).

Therefore, the only direct variation equation containing the ordered pair (2, 7) is y = 7/2x.