Final answer:
The correct equation representing the relationship between x and y, where y varies directly with x and y = 14 when x = 6, is y = 7x.
Step-by-step explanation:
The value of y varies directly with x, which means that as x increases, y increases at a constant rate, and as x decreases, y decreases at the same constant rate. This relationship is described by the linear equation y = kx, where k is the constant of variation. To find the constant of variation, we can use the given values, y = 14 when x = 6, which gives us 14 = k*6. Solving for k gives us k = 14/6, which simplifies to k = 7/3 or k = 2.33 (repeating). However, since we need to choose from given options, we look for a whole number ratio and 14/6 can be simplified to 7/3, but looking at the integer options, we deduce that k must be equal to 7 so that when x = 6, y = 14. Thus, the correct equation that represents the relationship between x and y is y = 7x.