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Let's solve this problem step by step.

The question asks to write the equation of a trend line using the points (1990, 253) and (2002, 320), and to estimate the attendance in 2005. The general form of the equation of a line is:

\[
y = mx + b
\]

Where:
- \( m \) is the slope.
- \( b \) is the y-intercept.

### Step 1: Calculate the Slope (\( m \))

The slope formula between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is:

\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

Using the points (1990, 253) and (2002, 320):
\[
m = \frac{320 - 253}{2002 - 1990} = \frac{67}{12} = 5.58
\]

### Step 2: Find the Y-Intercept (\( b \))

Now that we have the slope, we can use one of the points and substitute it into the equation \( y = mx + b \) to find \( b \). Let's use the point (1990, 253):

\[
253 = 5.58(1990) + b
\]

\[
253 = 11109.42 + b
\]

\[
b = 253 - 11109.42 = -10857.83
\]

### Step 3: Equation of the Line

So the equation of the trend line is:

\[
y = 5.58x - 10857.83
\]

### Step 4: Estimate the Attendance in 2005

Now, substitute \( x = 2005 \) into the equation to find the attendance:

\[
y = 5.58(2005) - 10857.83 = 11112.9 - 10857.83 = 255.07
\]

Thus, the estimated attendance in 2005 is approximately **255.07 million**.

### Correct Answer

Based on the given choices, the correct equation is:

\[
\boxed{B: \ y = 5.58x - 10857.83}
\]

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Do you need further details or have any questions?

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Here are 5 questions to expand your knowledge:
1. How do you find the slope of a line between two points?
2. What does the slope represent in the context of a real-world problem?
3. How would you interpret the y-intercept in this problem?
4. How can you use a trend line to make predictions?
5. Why is it important to round numbers to two decimal places in trend lines?

**Tip:** Always double-check units (like millions in this case) to ensure your interpretation of results is accurate.

The table shows the attendance in millions at theme parks in a certain country. Make a scatter plot of the data pairs, draw a trend line, and write its equation. Estimate the attendance at theme parks in the country in 2005.

Solve a problem involving the attendance at theme parks over the years. Learn how to calculate the trend line equation using linear equations and estimate future attendance values. Suitable for students in Grades 8-10.

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