Question

Use the drop-down menus to complete the statements to match the information shown by the graph. A graph has time (minutes) on the x-axis, and water in the pool (gallons) on the y-axis. A line labeled pool B goes through (0, 0) and has a positive slope. A line labeled pool A starts at a point above (0, 0) and has a positive slope. Pool A is filling up [Select One: faster/slower] than Pool B because the [Select One: slope/steepness] of the graph for Pool A is [Select One: greater/less] than that of the graph for Pool B. The [Select One: slope/steepness] of the graph tells you the unit rate in [Select One: gallons/minute].

Answer 1

Pool A is filling up faster than Pool B because the slope of the graph for Pool A is greater than that of the graph for Pool B. The slope of the graph tells you the unit rate in gallons per minute.

The slope of a line on a graph represents the rate of change between the two variables. In this case, the x-axis represents time in minutes, and the y-axis represents the amount of water in the pool in gallons. The positive slope of both Pool A and Pool B indicates an increase in the amount of water in the pool over time.

Now, when comparing the slopes of the two lines, the steeper the slope, the greater the rate of change. Since the slope of the graph for Pool A is greater than that of Pool B, it means that Pool A is filling up at a faster rate. This is because for every additional minute that passes, Pool A gains more gallons of water compared to Pool B.

In practical terms, the slope of the graph tells us the unit rate, which is the amount of water added per minute. If, for example, the slope of Pool A is 3 gallons per minute, and the slope of Pool B is 2 gallons per minute, it means that Pool A is filling up faster by 1 gallon per minute. Therefore, the greater slope of Pool A compared to Pool B indicates a faster rate of water filling in Pool A.