To solve this, we need to write the equation of the trend line based on the two yellow points shown on the scatter plot. The equation will be in slope-intercept form, $y = mx + b$, where:

• $m$ is the slope of the line.
• $b$ is the y-intercept.

Step 1: Identify the coordinates of the two yellow points

From the graph:

• The first yellow point is at $(3, 2)$.
• The second yellow point is at $(7, 6)$.

Step 2: Calculate the slope ($m$)

The slope formula is: $m = \frac{y_2 - y_1}{x_2 - x_1}$ Substitute the points $(x_1, y_1) = (3, 2)$ and $(x_2, y_2) = (7, 6)$: $m = \frac{6 - 2}{7 - 3} = \frac{4}{4} = 1$

So, the slope $m = 1$.

Step 3: Find the y-intercept ($b$)

Using the slope-intercept form $y = mx + b$, substitute $m = 1$ and one of the points, such as $(3, 2)$: $2 = 1(3) + b$ $2 = 3 + b$ $b = 2 - 3 = -1$

Step 4: Write the equation

The equation of the line is: $y = 1x - 1 \quad \text{or simply} \quad y = x - 1$

Final Answer:

The equation of the trend line is: $y = x - 1$

Would you like more clarification, or do you have further questions? Here are 5 follow-up questions to consider:

1. What does the slope of the line represent in this context?
2. How would the equation change if the points were different?
3. What are some real-world applications of finding trend lines in scatter plots?
4. How can we confirm that the trend line fits the data well?
5. Can you describe how to calculate the y-intercept when given only the slope and one point?

Tip: Always double-check your calculations by substituting both points into your final equation to verify correctness!