Question

the function graphed represents the amount of water in a container, in gallons, x minutes after a drain is opened. what is the meaning of each key feature of the graph? drag the answer into the box to match each item. x - intercept y - intercept

Explanation:

• x - intercept: The x - intercept is the point where the graph crosses the x - axis, which means \(y = 0\) (amount of water is 0 gallons). From the graph, when \(y = 0\), \(x\) (time in minutes) is the time when the container is empty. Looking at the graph, the x - intercept is at \(x=15\) (assuming the grid, since from (0,120) to (15,0) as the line goes from (0,120) to (15,0) approximately, but from the given graph, the x - intercept is at \(x = 15\)? Wait, the graph shows the line from (0,120) to (15,0)? Wait, the x - axis has marks at 0,10,20,30. Wait, the line goes from (0,120) down to (15,0)? Wait, no, the graph's x - intercept is at \(x = 15\)? Wait, actually, the y - intercept is at (0,120), which is when \(x = 0\) (time = 0 minutes), so the amount of water at time 0 is 120 gallons. The x - intercept is when \(y=0\), so the time when the container has 0 gallons of water, which is the time when the container is empty.
• y - intercept: The y - intercept is the point where the graph crosses the y - axis, which is when \(x = 0\) (time = 0 minutes). So the y - intercept (0,120) means that at 0 minutes (when the drain is opened), the amount of water in the container is 120 gallons.

So for x - intercept: the time when the container is empty (when the amount of water is 0 gallons). For y - intercept: the amount of water in the container when the drain is opened (at 0 minutes).

Answer:

• x - intercept: The time (in minutes) when the container is empty (has 0 gallons of water).
• y - intercept: The amount of water (in gallons) in the container when the drain is opened (at 0 minutes).