Final answer:
The question mistakenly asks for the constant of proportionality from y to z but provides a proportional relationship between x and y. The constant of proportionality for x to y would be 3.5, but the relationship between y and z cannot be determined without additional information.
Step-by-step explanation:
The question is asking for the constant of proportionality between the variables y and z, given the proportional relationship x = 7/2y. However, there seems to be a typo in the question as the variable z is not mentioned in the provided equation, and therefore, we can't determine the relationship between y and z directly from the given information. Typically, proportional relationships follow the form y = kx, where k is the constant of proportionality. If the relationship were between x and y, given the equation x = 7/2y, the constant of proportionality from y to x would be 7/2 or 3.5, meaning for every unit increase in y, x increases by 3.5 units.
This concept of proportional relationships also applies to linear relationships, where a graph of two directly proportional variables will show a straight line through the origin (0, 0). It is essential to understand the differences between direct and inverse proportionality. While direct proportion means the variables increase or decrease together, inverse proportion means as one variable increases, the other decreases, and this is often represented with an equation of the form y = k/x.