The question asks for the equation of the trend line passing through the two yellow points in slope-intercept form ($y = mx + b$).

Step 1: Identify the coordinates of the two points

From the graph:

• Point 1: $(4, 1)$
• Point 2: $(10, 7)$

Step 2: Calculate the slope ($m$)

The slope formula is: $m = \frac{y_2 - y_1}{x_2 - x_1}$ Substitute the coordinates: $m = \frac{7 - 1}{10 - 4} = \frac{6}{6} = 1$

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

Using the slope $m = 1$ and one of the points (e.g., $(4, 1)$), substitute into the equation $y = mx + b$: $1 = 1(4) + b$ $b = 1 - 4 = -3$

Final Equation

$y = x - 3$

Would you like a detailed breakdown of slope calculations or have further questions?

Relative Questions:

1. How do we interpret the slope in the context of scatterplots?
2. Can you find the equation of a line if it passes through one point and is parallel to another line?
3. What is the significance of the y-intercept in this problem?
4. How can outliers affect the line of best fit?
5. How would the equation change if we had a steeper slope?

Tip: When calculating the slope, always simplify the fraction for clarity!