Final answer:
To find the direct variation equation, we determine the constant k by plugging in the given values of x and y and solving for k, resulting in the equation y = (7/6)x.
Step-by-step explanation:
Given that y varies directly with x, we know that the relationship between y and x can be described by an equation of the form y = kx, where k is the constant of variation. To find the value of k, we use the information that when x is 12, y is 14.
Substituting these values into the equation, we get:
14 = k(12)
By dividing both sides by 12, we can solve for k:
k = 14 / 12 = 7 / 6
Therefore, the equation that represents the direct variation between x and y is:
y = (7/6)x
This answer corresponds to choice (b) in the provided options.