To find the best linear equation that models the population of the town from 2000 to 2010 based on the scatter plot, we need to determine the slope (rate of change) and y-intercept of the line that best fits the data.

Step 1: Identify two points from the graph

From the scatter plot, two clear points can be:

• At $t = 0$ (Year 2000), $P(0) = 1.12$ thousand.
• At $t = 10$ (Year 2010), $P(10) = 1.32$ thousand.

Step 2: Calculate the slope $m$

The slope of a linear equation $P(t) = mt + b$ is given by:

$m = \frac{\Delta P}{\Delta t} = \frac{P(10) - P(0)}{10 - 0} = \frac{1.32 - 1.12}{10 - 0} = \frac{0.20}{10} = 0.02$

So, the slope $m = 0.02$.

Step 3: Identify the y-intercept $b$

The y-intercept $b$ is the population at $t = 0$, which is 1.12.

Step 4: Form the equation

The equation of the line is:

$P(t) = 0.02t + 1.12$

Conclusion:

The correct linear equation that models the town's population from 2000 to 2010 is: $P(t) = 0.02t + 1.12$

This matches the second option from the given choices.

Would you like a more detailed explanation of any step? Here are some related questions you might want to explore:

1. What is the importance of finding the slope in a linear equation?
2. How does the y-intercept relate to real-world data in this context?
3. What are the units of the slope in this problem?
4. How would the equation change if the growth rate were faster?
5. How could we model the population beyond 2010 with this equation?

Tip: When analyzing scatter plots, always identify two clear points to calculate the slope accurately.