Final answer:
The slope of the graph representing the number of vehicles passing through a fast food drive-through window over time is the rate at which the vehicles are served, which in this case is 4 vehicles per minute. When drawing a line for a car traveling twice as fast, the slope would be 8 vehicles per minute. For position versus time graphs, the slope represents average velocity, and the y-intercept represents the initial position
Step-by-step explanation:
If a fast food drive-through window has at most 360 vehicles drive through in 90 minutes, and this relationship is represented by a graph, then the slope represents the rate at which the vehicles are served over time. In this case, the slope is the number of vehicles (360) divided by the time in minutes (90), yielding 4 vehicles per minute. Therefore, the slope of the graph would be 4.
If you were to draw this on a graph, the y-axis would represent the number of vehicles, and the x-axis would represent the time in minutes. If a car travels twice as fast, meaning it serves twice the number of vehicles in the same amount of time, the slope of the new line would be twice the original slope, meaning 8 vehicles per minute. This line would also start at the origin (0,0), since at time zero, no vehicles have been served.
When labeling graphs such as position versus time or displacement versus time, the slope usually represents velocity or speed. For example, the slope in the context of position vs. time is average velocity, and the intercept is the position or displacement at time zero. Consequently, labeling a graph includes the initial point, also known as the y-intercept, and would follow the convention of the equation y = mx + b, where m is the slope and b is the y-intercept.
When discussing maximums and minimums in the context of graphs, these are typically points where the graph reaches its highest or lowest value, respectively. However, in the context of a fast-food drive-through window or a car's position over time graph, you would not usually discuss maxima and minima unless the question specifically pertains to them, such as with acceleration graphs.