Question

The graph below shows how the amount of water in a bathtub is changing over time.



Which equation describes the relationship between x, the time in minutes, and y, the amount of water in gallons?

Answer 1

To determine the equation that describes the relationship between time \( x \) (in minutes) and the amount of water \( y \) (in gallons) in a bathtub, we typically need to analyze the characteristics of the graph.

1. **Identify Key Points**: Look for two distinct points on the graph. For example, if \( (0, 0) \) indicates that at time 0 minutes there are 0 gallons of water, and if at \( (5, 10) \) there's 10 gallons at 5 minutes.

2. **Determine the Slope**: The slope \( m \) can be calculated using the formula:
\[
m = \frac{\Delta y}{\Delta x} = \frac{y_2 - y_1}{x_2 - x_1}
\]
For the points mentioned:
\[
m = \frac{10 - 0}{5 - 0} = \frac{10}{5} = 2
\]

3. **Form the Equation**: With the slope calculated, the linear equation can be written in the slope-intercept form \( y = mx + b \). If the y-intercept \( b \) is 0 (since it starts at 0 when time is 0), the equation simplifies to:
\[
y = 2x
\]

Using these steps would allow you to determine the correct linear equation. If you can provide specific points or characteristics from the graph, then I could give you a more precise equation.