Question

what does the slope of the line tell you about the situation? the water was 40 inches deep before julian started draining it. the water was 20 inches deep after julian had drained 300 gallons. the water’s depth decreased 15 inches for every gallon of water drained. the water’s depth decreased 1 inch for every 15 gallons of water drained.

Explanation:

Step1: Recall slope formula

The slope \( m \) of a line is given by \( m=\frac{\Delta y}{\Delta x} \), where \( \Delta y \) is the change in the \( y \)-variable (water depth in inches) and \( \Delta x \) is the change in the \( x \)-variable (gallons of water drained).

Step2: Identify two points

From the graph, we can use the points \( (0, 40) \) (when 0 gallons are drained, depth is 40 inches) and \( (300, 20) \) (when 300 gallons are drained, depth is 20 inches).

Step3: Calculate the slope

\( \Delta y = 20 - 40=- 20 \) inches (negative because depth is decreasing), \( \Delta x=300 - 0 = 300 \) gallons.
So, \( m=\frac{-20}{300}=-\frac{1}{15} \) inches per gallon. This means for every 15 gallons drained (\( \Delta x = 15 \)), the depth decreases by 1 inch (\( \Delta y=- 1 \)).

Step4: Analyze each option

• Option 1: "The water was 40 inches deep before Julian started draining it." This is the \( y \)-intercept, not the slope, so incorrect.
• Option 2: "The water was 20 inches deep after Julian had drained 300 gallons." This is a point on the line, not the slope, so incorrect.
• Option 3: "The water’s depth decreased 15 inches for every gallon of water drained." The slope we calculated is \( -\frac{1}{15} \), not - 15, so incorrect.
• Option 4: "The water’s depth decreased 1 inch for every 15 gallons of water drained." This matches our slope interpretation (since slope is \( -\frac{1}{15} \), meaning 1 inch decrease per 15 gallons drained), so correct.

Answer:

The water’s depth decreased 1 inch for every 15 gallons of water drained.