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?

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.