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To find the equation of the trend line in slope-intercept form (\(y = mx + b\)), we need to determine both the slope \(m\) and the y-intercept \(b\) of the red line drawn through the scatter plot points.

### Step 1: Estimate the Slope (m)
The slope \(m\) represents the "rise over run." By identifying two clear points on the line, we can calculate \(m\) as:
\[
m = \frac{{y_2 - y_1}}{{x_2 - x_1}}
\]

Looking at the line, let’s approximate two points that it seems to pass through:
1. Near \( (1, 12) \)
2. Near \( (8, 24) \)

Using these points:
\[
m = \frac{{24 - 12}}{{8 - 1}} = \frac{12}{7} \approx 1.71
\]

### Step 2: Estimate the y-Intercept (b)
The y-intercept \(b\) is the value of \(y\) when \(x = 0\). Observing the line, it seems that it intersects the y-axis just below 10, around \(b \approx 10\).

### Step 3: Write the Equation
With \(m \approx 1.71\) and \(b \approx 10\), the equation of the trend line is:
\[
y \approx 1.71x + 10
\]

This is an approximation based on visual inspection. 

Would you like a detailed breakdown of each calculation or have any questions?

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### Related Questions:
1. What is the interpretation of the slope in a trend line?
2. How can we refine estimates of slope and intercept if we have more precise data points?
3. How does a trend line help in predicting future values?
4. What is the significance of a positive slope versus a negative slope?
5. How does changing the y-intercept affect the position of the line on the graph?

### Tip:
When estimating a trend line visually, select points that lie directly on the line if possible, to improve accuracy.

Write an equation in slope-intercept form of the trend line for the scatter plot shown.

Learn how to find the equation of a trend line in slope-intercept form for a given scatter plot. This example includes calculating the slope using points on the trend line and estimating the y-intercept. Suitable for students in Grades 8-10.

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