Final answer:
The equation y = kx represents the direct variation between x and y. By substituting the given values into the equation, we can determine the constant of variation and find the value of y for a given x.
Step-by-step explanation:
The problem states that x and y vary directly, which means they have a linear relationship and can be represented by the equation y = kx, where k is the constant of variation.
Using the information given in the problem, we can determine the value of k. When x is 13, y is 52, so substituting these values into the equation, we have 52 = 13k. Solving for k, we get k = 52/13 = 4.
Now we can use the equation y = 4x to find y when x is 14. Substituting x = 14 into the equation, we have y = 4(14) = 56.