Final answer:
The graph does show a proportional relationship, as indicated by the straight line passing through the origin (0, 0), reflecting a consistent rate of change between distance and time.
Step-by-step explanation:
In mathematics, a proportional relationship exists when two quantities vary in such a way that one of the quantities is a constant multiple of the other. In other words, as one quantity increases or decreases, the other quantity changes in direct proportion to it.
To determine if the graph shows a proportional relationship, we look at whether the graphed data forms a straight line passing through the origin (0, 0). If it does, this indicates a direct proportional relationship between the two quantities. In this context, because the line begins at point (0, 0) and continues to the right, it suggests that the variables distance (miles) and time (hours) are in direct proportion, meaning that as one increases, the other does as well at a consistent rate.
The general form of a linear equation in this context is y = mx + b, where m represents the slope and b represents the y-intercept. Since the graph passes through the origin, b is zero, simplifying the equation to y = kx, where k is the constant of proportionality. A graph of displacement versus time like this is common in physics, where time is usually the independent variable, and displacement or distance is the dependent variable.