A bathtub is filled with 40 gallons of water. The water starts draining out of the tub at a rate of 8 gallons per minute. Choose the sketch of a graph that shows the relationship between the number of minutes since the tub started draining and the number of gallons of water in the tub.(1 point) Responses Image with alt text: A coordinate plane shows the x-axis representing Number of Minutes, ranging from 0 to 7 in increments of 1. The y-axis represents the Number of Gallons of Water in Tub, ranging from 0 to 50 in increments of 5. A straight line connects the following two plotted points: left parenthesis 8 comma 0 right parenthesis and left parenthesis 0 comma 40 right parenthesis. Image with alt text: A coordinate plane shows the x-axis representing Number of Minutes, ranging from 0 to 7 in increments of 1. The y-axis represents the Number of Gallons of Water in Tub, ranging from 0 to 50 in increments of 5. A concave upward curve connects the following two plotted points: left parenthesis 5 comma 0 right parenthesis and left parenthesis 0 comma 40 right parenthesis. It passes through left parenthesis 4 comma 1 right parenthesis, and left parenthesis 1 comma 16 right parenthesis. Values are approximate. Image with alt text: A coordinate plane shows the x-axis representing Number of Minutes, ranging from 0 to 7 in increments of 1. The y-axis represents the Number of Gallons of Water in Tub, ranging from 0 to 50 in increments of 5. A straight line connects the following two plotted points: left parenthesis 5 comma 0 right parenthesis and left parenthesis 0 comma 40 right parenthesis. Image with alt text: A coordinate plane shows the x-axis representing Number of Minutes, ranging from 0 to 7 in increments of 1. The y-axis represents the Number of Gallons of Water in Tub, ranging from 0 to 50 in increments of 5. A concave downward curve connects the following two plotted points: left parenthesis 5 comma 0 right parenthesis and left parenthesis 0 comma 40 right parenthesis. It passes through left parenthesis 4 comma 25 right parenthesis, and left parenthesis 2 comma 37 right parenthesis. Values are approximate. Remaining Attempts : 3 Skip to navigation

Question

A: A coordinate plane shows the x-axis representing Number of Minutes, ranging from 0 to 7 in increments of 1. The y-axis represents the Number of Gallons of Water in Tub, ranging from 0 to 50 in increments of 5. A straight line connects the following two plotted points: left parenthesis 8 comma 0 right parenthesis and left parenthesis 0 comma 40 right parenthesis.

B: alt="A coordinate plane shows the x-axis representing Number of Minutes, ranging from 0 to 7 in increments of 1. The y-axis represents the Number of Gallons of Water in Tub, ranging from 0 to 50 in increments of 5. A concave upward curve connects the following two plotted points: left parenthesis 5 comma 0 right parenthesis and left parenthesis 0 comma 40 right parenthesis. It passes through left parenthesis 4 comma 1 right parenthesis, and left parenthesis 1 comma 16 right parenthesis. Values are approximate."

C: alt="A coordinate plane shows the x-axis representing Number of Minutes, ranging from 0 to 7 in increments of 1. The y-axis represents the Number of Gallons of Water in Tub, ranging from 0 to 50 in increments of 5. A straight line connects the following two plotted points: left parenthesis 5 comma 0 right parenthesis and left parenthesis 0 comma 40 right parenthesis. "

D: A coordinate plane shows the x-axis representing Number of Minutes, ranging from 0 to 7 in increments of 1. The y-axis represents the Number of Gallons of Water in Tub, ranging from 0 to 50 in increments of 5. A concave downward curve connects the following two plotted points: left parenthesis 5 comma 0 right parenthesis and left parenthesis 0 comma 40 right parenthesis. It passes through left parenthesis 4 comma 25 right parenthesis, and left parenthesis 2 comma 37 right parenthesis. Values are approximate.

Answer 1

To determine the correct graph for the scenario where a bathtub is filled with 40 gallons of water and drains at a rate of 8 gallons per minute, we will model the relationship between time in minutes and the amount of water remaining in the tub.

1. The bathtub starts with 40 gallons.
2. It drains at a constant rate of 8 gallons per minute.

The equation that represents the amount of water (W) left in the tub after t minutes is:

\[ W(t) = 40 - 8t \]

This is a linear equation where:

• The y-intercept (at t = 0) is 40 gallons.
• The slope (rate of change) is -8 gallons per minute, indicating that the water decreases by 8 gallons for every minute that passes.

To find when the tub will be empty, we set W(t) = 0: \[ 40 - 8t = 0 \] \[ 8t = 40 \] \[ t = 5 \]

Thus, the tub will be empty after 5 minutes.

Considering the options:

• Option A shows a line from (8, 0) to (0, 40), which doesn't represent the correct linear relationship.
• Option B reflects a curve, which does not apply since the drain rate is constant.
• Option C indicates a line between (5, 0) and (0, 40), which is a straight line showing the right relationship.
• Option D also shows a curve, which again wouldn't represent a constant drain rate.

Thus, the correct choice is Option C. This graph shows a straight line from 40 gallons at time 0 to 0 gallons at time 5, accurately representing the draining process.