Final answer:
In a proportional relationship, the slope of the linear equation represents the unit rate, describing how changes in the independent variable affect the dependent variable.
Step-by-step explanation:
In a proportional relationship, the value that remains the same as the unit rate is the slope. When we represent such a relationship with a linear equation in slope-intercept form (y = mx + b), the slope (m) describes how the dependent variable (y) changes for every one-unit increase in the independent variable (x). For a proportional relationship, specifically one where the line passes through the origin, the equation simplifies to y = kx, with k being the slope and the proportionality constant. There is no y-intercept term (b) because the line crosses the y-axis at the origin (0,0). Therefore, the unit rate, which is the change in the dependent variable (y) with respect to one unit of change in the independent variable (x), is indeed the slope of the line.