Final answer:
The constant of proportionality in the directly proportional relationship where y=14 when x=7 is 2. This is found by dividing 14 by 7, yielding the constant of proportionality k=2.
Step-by-step explanation:
When variables are in a directly proportional relationship, it means that as one variable changes, the other changes at a constant rate. This constant rate is known as the constant of proportionality, often represented by the symbol k. The formula for direct proportionality is y = kx, where x is the independent variable and y is the dependent variable.
To find the constant of proportionality when y is 14 and x is 7, we set up the equation according to the direct proportionality, so y = kx becomes 14 = k(7). We then divide both sides by 7 to solve for k: k = 14 / 7 = 2. Therefore, the constant of proportionality is 2, which corresponds to option a) 2.