The correct answer is: Y= 2/3x. Hence the correct option is c.
To determine which equation has a greater rate, we can look at the coefficients of the x terms in each equation. The equation Y= 2/3 x has a coefficient of 2/3, indicating that for every increase of 1 unit in x, Y increases by 2/3 units. On the other hand, the equation Y= 1/4x has a coefficient of 1/4 , indicating a lower rate of increase.
Therefore, relationship b, represented by the equation Y= 2/3x, has a greater rate than relationship a, which is represented by the other equations provided. The steeper slope of the line in relationship b suggests a faster increase in the dependent variable Y relative to the independent variable x. Hence the correct option is c.