Question

depth of
0.4
0.3
0.2
0.1
0.25 0.5 0.75 1 1.25 1.5 1.75 2 2.25 2.5
hours of rain
what does the slope of the line tell you about the situation?
the bucket can hold 0.7 inches of water.
the storm lasts 2.5 hours.
the depth of the water in the bucket increases 1 inch every 4 hours.
the depth of the water in the bucket increases 4 inches every hour.

Explanation:

Step1: Recall Slope Formula

Slope \( m = \frac{\Delta y}{\Delta x} \), where \( \Delta y \) is change in depth, \( \Delta x \) is change in time (hours).

Step2: Identify Points

Take two points, e.g., (0, 0) and (4, 1) (or from graph: at \( x = 1.25 \), \( y = 0.3 \); \( x = 0.5 \), \( y = 0.1 \)). Calculate slope: \( \frac{0.1}{0.5} = 0.25 \) or \( \frac{1}{4} \). So depth increases \( \frac{1}{4} \) inch per hour, meaning 1 inch every 4 hours.

Step3: Evaluate Options

• "Bucket holds 0.7 inches": Slope ≠ capacity. Incorrect.
• "Storm lasts 2.5 hours": Slope ≠ duration. Incorrect.
• "Depth increases 1 inch every 4 hours": Matches slope \( \frac{1}{4} \) in/hour (1 inch over 4 hours). Correct.
• "4 inches every hour": Slope is 0.25, not 4. Incorrect.

Answer:

The depth of the water in the bucket increases 1 inch every 4 hours.