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) Graph 1,2,3,4?

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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 straight line connects the following two plotted points: left parenthesis 5 comma 0 right parenthesis and left parenthesis 0 comma 40 right parenthesis.

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 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.

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 straight line connects the following two plotted points: left parenthesis 8 comma 0 right parenthesis and left parenthesis 0 comma 40 right parenthesis.

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.
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.
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Answer 1

To determine which graph accurately represents the scenario of the bathtub draining, we need to analyze the situation:

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

We can calculate how long it will take for the tub to empty completely. At a rate of 8 gallons per minute, it will take:

\[ \text{Time to empty} = \frac{40 \text{ gallons}}{8 \text{ gallons/minute}} = 5 \text{ minutes} \]

So, after 0 minutes, there are 40 gallons; after 1 minute, there will be 32 gallons; after 2 minutes, there will be 24 gallons; after 3 minutes, there will be 16 gallons; after 4 minutes, there will be 8 gallons; and after 5 minutes, there will be 0 gallons.

The relationship is linear, meaning the amount of water decreases at a constant rate. Therefore, the graph should be a straight line that starts at (0, 40) and ends at (5, 0).

Analyzing the options:

1. First option: Straight line from (0, 40) to (5, 0). This is a correct representation.
2. Second option: Concave upward curve from (0, 40) to (5, 0). This is incorrect since the water isn't draining gradually slower.
3. Third option: Straight line from (0, 40) to (8, 0). This is also incorrect because it should end at (5, 0), not (8, 0).
4. Fourth option: Concave downward curve from (0, 40) to (5, 0). This is incorrect since the water is draining at a constant rate.

Based on this analysis, the correct graph representing the relationship between the minutes and gallons of water in the tub is the first option.