Final answer:
Equation a. y = 2.5x represents a directly proportional relationship since its y-intercept is 0 and would graph as a line through the origin. Equation b. y = x - 4 is non-proportional due to a non-zero y-intercept, indicating the ratio of y to x is not constant.
Step-by-step explanation:
To determine whether each equation represents a proportional or non-proportional relationship, we can look at the format of the given equations and compare them to the standard linear equation form y = mx + b, where m is the slope and b is the y-intercept.
For a. y = 2.5x, this equation is of the form y = kx (where k is a constant), which indicates a directly proportional relationship. This is because the y-intercept, b, is 0, which means if we were to express this equation graphically, the line would pass through the origin (0, 0).
For b. y = x - 4, this equation is of the form y = mx + b with a y-intercept b not equal to 0. This indicates a non-proportional relationship since the line would not pass through the origin and the ratio of y to x changes as we move along the line.