The problem asks to find the equation of the trend line using the two yellow points shown in the scatter plot. The equation should be written in slope-intercept form, $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.

Steps to solve:

1. Identify the two yellow points:

   • The first yellow point is at $(1, 2)$.
   • The second yellow point is at $(7, 5)$.

2. Calculate the slope (m): The slope formula is: $m = \frac{y_2 - y_1}{x_2 - x_1}$ Using the points $(1, 2)$ and $(7, 5)$: $m = \frac{5 - 2}{7 - 1} = \frac{3}{6} = \frac{1}{2}$

3. Find the y-intercept (b): Using the slope $m = \frac{1}{2}$ and one of the points (we'll use $(1, 2)$), substitute into the slope-intercept form equation: $y = mx + b$ Plugging in the values: $2 = \frac{1}{2}(1) + b$ Simplifying: $2 = \frac{1}{2} + b$ $b = 2 - \frac{1}{2} = \frac{4}{2} - \frac{1}{2} = \frac{3}{2}$

4. Write the equation: The equation of the trend line is: $y = \frac{1}{2}x + \frac{3}{2}$

Would you like a further breakdown of these steps or explanations?

Related Questions:

1. How do you interpret the meaning of the slope in the context of this scatter plot?
2. What does the y-intercept tell us about the data in this plot?
3. How would the equation change if one of the points was slightly different?
4. Can you use other points on the line to verify the slope?
5. How could this line be used to predict future data points?

Tip:

Remember, the slope $m$ represents the rate of change, or how much $y$ changes for each unit increase in $x$.