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To solve this problem, we’ll follow these steps:

1. **Identify Key Details in the Graph**: The graph shows the depth of snow \( S \) on Kayden's lawn (y-axis) over time \( t \) (x-axis). We can observe that it is a straight line, suggesting a linear equation of the form \( S = mt + b \), where \( m \) is the slope, and \( b \) is the y-intercept.

2. **Find the Slope \( m \)**:
   - From the graph, it appears that the depth decreases at a constant rate, indicating a steady rate of melting.
   - The slope \( m \) represents the rate of change of snow depth over time.
   - To find the slope, pick two points on the line, such as \( (0, 12) \) and \( (4, 0) \).
   - Slope \( m = \frac{\Delta S}{\Delta t} = \frac{0 - 12}{4 - 0} = -3 \).

3. **Determine the Equation**:
   - With \( m = -3 \) and the initial depth \( S = 12 \) at \( t = 0 \), the equation becomes:
     \[
     S = -3t + 12
     \]

4. **Find and Interpret the y-Intercept**:
   - The y-intercept \( b = 12 \) represents the initial depth of snow on Kayden's lawn when \( t = 0 \) (when the snow stopped falling).
   - This means there were initially 12 inches of snow on the lawn.

### Final Answer:
- **Equation**: \( S = -3t + 12 \)
- **y-Intercept**: \( 12 \), which indicates that there were 12 inches of snow when the snow stopped falling.

Would you like more details on any part of the solution, or do you have further questions?

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Here are some related questions for practice:

1. How would the equation change if the snow melted at a different rate?
2. If the snow had started at 15 inches instead of 12, what would the equation be?
3. What does the slope represent in a real-world context?
4. How would you interpret a positive slope in this scenario?
5. How long would it take for all the snow to melt if the rate doubled?

**Tip**: When interpreting slopes, remember that a negative slope represents a decrease over time, while a positive slope would indicate an increase.

At the end of a snowstorm, Kayden saw there was a lot of snow on his front lawn. The temperature increased, and the snow began to melt at a steady rate. Let S represent the depth of snow on Kayden’s lawn, in inches, t hours after the snow stopped falling. A graph of S is shown. Write an equation for S, then state the y-intercept of the graph and determine its interpretation in the context of the problem.

Explore how to write a linear equation for the depth of snow on Kayden's lawn as it melts over time. Understand how to find the slope and y-intercept of the graph and interpret them in a real-world context. Suitable for students in Grades 7-9.

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