Final answer:
Directly proportional relationships are represented by the equation y = kx, where k is the constant of proportionality. For a constant greater than 1, y = 2.25x exemplifies this. For a constant less than 1, y = 0.11x is an example.
Step-by-step explanation:
In mathematics, when we say two values are directly proportional, it means that as one value increases, the other value increases at a constant rate, which is described by the constant of proportionality. The equation for a linear relationship with direct proportionality takes the form of y = kx, where k is the constant of proportionality.
a. An equation that has a constant of proportionality greater than 1 is y = 2.25x, which means that for every unit increase in x, y increases by 2.25 units.
b. An equation with a constant of proportionality less than 1 is y = 0.11x, indicating that y increases by 0.11 units for every unit increase in x.