To solve this, we need to find the linear function that relates the distance $d$ to time $t$. The problem provides:

1. At $t = 0$, $d = 0$ (since the car just passed the timing device).
2. At $t = 9$ seconds, $d = 891$ feet.

Step 1: Find the slope of the line

The slope $m$ of a linear function is calculated as: $m = \frac{\Delta d}{\Delta t} = \frac{d_2 - d_1}{t_2 - t_1}$ Here: $m = \frac{891 - 0}{9 - 0} = \frac{891}{9} = 99$

Step 2: Write the equation of the line

The general equation of a linear function is: $d = mt + b$ Here:

• $m = 99$ (calculated slope)
• $b = 0$ (since at $t = 0$, $d = 0$).

Final Answer:

The linear function is: $d = 99t$

This function models the distance $d$ the car has traveled in feet after $t$ seconds.

Do you have any questions or want further clarification?

Here are 5 related questions to expand understanding:

1. How would the equation change if the car started 500 feet ahead of the timing device?
2. What does the slope $m$ represent in real-world terms?
3. How would you find the distance traveled after 15 seconds using the linear function?
4. How would the equation change if the car were moving at a different constant speed?
5. Could you use this equation to determine the time it takes to travel a specific distance?

Tip: In a linear function, the slope $m$ always represents the rate of change between the two variables.