Let’s solve this! The goal is to find the equation of the trend line using the two given blue points. The equation will be in slope-intercept form, $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.

Steps:

1. Identify the two blue points. From the image:

   • The first blue point is approximately $(5, 1)$.
   • The second blue point is approximately $(7, 7)$.

2. Calculate the slope $m$: The slope formula is: $m = \frac{y_2 - y_1}{x_2 - x_1}$ Substituting the coordinates of the two points: $m = \frac{7 - 1}{7 - 5} = \frac{6}{2} = 3$

3. Find the y-intercept $b$: Use the equation $y = mx + b$ and substitute one of the points (e.g., $(5, 1)$) and the slope $m = 3$: $1 = 3(5) + b$ Simplify: $1 = 15 + b \quad \Rightarrow \quad b = 1 - 15 = -14$

4. Write the equation: Substituting $m = 3$ and $b = -14$, the equation of the trend line is: $y = 3x - 14$

Would you like further clarifications? Here are some related questions for practice:

1. How do you verify if the trend line equation works for other points on the graph?
2. Can you rewrite the equation in standard form $Ax + By = C$?
3. What does the slope represent in real-life data scenarios?
4. How can you determine if a scatter plot shows a strong or weak correlation?
5. What changes in the equation if the slope is negative?

Tip: Always double-check the coordinates of points to ensure accurate calculations!