The constant of proportionality in the equation y = 4/5x is 4/5. This represents the fixed rate at which y changes in relation to changes in x, in a directly proportional relationship.
The constant of proportionality in the equation y = \(\frac{4}{5}\)x is found directly in the equation. This constant k shows the relationship between y and x in a directly proportional relationship, where the value of y changes in direct relation to the change in x. Because the equation is of the form y = kx, the constant of proportionality is simply the coefficient of x, which is \(\frac{4}{5}\).
In proportional relationships, when one variable increases, the other variable increases at a constant rate, hence the straight-line graph through the origin that would represent this relationship. Consequently, the answer to the question is option (a) \(\frac{4}{5}\), making this the constant of proportionality for the equation y = \(\frac{4}{5}\)x.
The constant of proportionality for the given equation is \(\frac{4}{5}\), as it defines the rate at which y increases for every unit increase in x.