To solve these questions, let’s examine the given equation:

$S(t) = -1.75t + 14$

where $S(t)$ is the depth of snow in inches, and $t$ is the time in hours after the snow stopped falling.

Part (c) - How much snow was melting per hour?

The rate at which the snow is melting per hour is represented by the coefficient of $t$ in the equation $S(t) = -1.75t + 14$. Here, the term $-1.75$ indicates the rate of snow melting per hour.

So, the snow was melting at a rate of 1.75 inches per hour.

Part (d) - How long will it take for the snow to completely melt?

To find when the snow completely melts, we need to determine when $S(t) = 0$, since that represents the snow depth reaching zero.

1. Set up the equation: $-1.75t + 14 = 0$

2. Solve for $t$: $-1.75t = -14$ $t = \frac{-14}{-1.75} = 8$

So, it will take 8 hours for the snow to completely melt.

Label for Answer (d)

Since $t = 8$ is the time, this answer is represented by the x-intercept of the line (since the snow depth reaches zero at this point).

Would you like a further breakdown of each part? Here are some related questions to explore:

1. What does the y-intercept of the line represent in this context?
2. How would the equation change if the snow were melting faster?
3. If the temperature drops and the snow starts accumulating again, how would we modify the equation?
4. What if the rate of melting were not constant but instead decreased over time?
5. How would you graph this equation, and what key points would you label?

Tip: When interpreting linear equations in real-world contexts, the slope often represents a rate of change, and the y-intercept represents the starting value.