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The graph titled "Taking a Shower" shows the relationship between the number of **minutes (x)** spent showering and the amount of **gallons (y)** of water used. The graph represents a linear relationship, as indicated by the straight line.

Key observations:
1. The point \((62, 139.5)\) is marked on the graph. This means that after 62 minutes, approximately 139.5 gallons of water have been used.
2. The line starts from the origin \((0, 0)\), suggesting that no water is used when no time is spent in the shower.
3. The slope of the line represents the rate of water usage in gallons per minute.

To analyze the situation further, we can find the slope and the equation of the line.

**Slope (m):**
The slope is calculated using two points on the line, in this case, the origin \((0, 0)\) and \((62, 139.5)\):

\[
m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{139.5 - 0}{62 - 0} = \frac{139.5}{62} \approx 2.25 \, \text{gallons per minute}
\]

Thus, the rate of water usage is approximately 2.25 gallons per minute.

**Equation of the Line:**
Since the line passes through the origin \((0, 0)\), the equation follows the form \(y = mx\). Substituting the slope \(m = 2.25\):

\[
y = 2.25x
\]

This equation means that for every minute spent showering, 2.25 gallons of water are used.

Would you like further details on this or have any specific questions?

Here are 5 related questions to consider:
1. How many gallons of water would be used after a 30-minute shower?
2. If 180 gallons of water are used, how long was the shower?
3. What is the practical significance of the slope in this context?
4. How would the graph change if the rate of water usage increased?
5. What would the equation look like if there was a base amount of water used regardless of time?

**Tip:** The slope of a line in real-life scenarios often represents a rate of change, such as speed or in this case, water usage per minute.

What is the relationship between the time spent showering and the water usage, and how can we find the slope and equation of the line from the graph?

Understand how to calculate the water usage during a shower based on the time spent. The linear equation derived from the graph shows a water usage rate of 2.25 gallons per minute. Suitable for students in Grades 8-10.

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