Let's analyze the image and solve the problem.

The two yellow points given on the scatter plot are:

1. Point 1: $(4, 6)$
2. Point 2: $(7, 1)$

We are tasked to find the equation of the trend line in slope-intercept form: $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.

Step 1: Calculate the slope ($m$)

The formula for slope is: $m = \frac{y_2 - y_1}{x_2 - x_1}$

Substitute the coordinates of the two points: $m = \frac{1 - 6}{7 - 4} = \frac{-5}{3}$

So, the slope is: $m = -\frac{5}{3}$

Step 2: Use the slope and one point to find the y-intercept ($b$)

The slope-intercept form is: $y = mx + b$

Choose one of the points, say $(4, 6)$, and substitute $x = 4$, $y = 6$, and $m = -\frac{5}{3}$: $6 = -\frac{5}{3}(4) + b$

Simplify: $6 = -\frac{20}{3} + b$

Convert $6$ to a fraction with denominator 3: $\frac{18}{3} = -\frac{20}{3} + b$

Solve for $b$: $b = \frac{18}{3} + \frac{20}{3} = \frac{38}{3}$

Step 3: Write the final equation

The equation of the trend line is: $y = -\frac{5}{3}x + \frac{38}{3}$

Would you like me to break this down further or explain any step in more detail?

5 Related Questions:

1. How can you check if a point lies on the line $y = -\frac{5}{3}x + \frac{38}{3}$?
2. What does the slope $m = -\frac{5}{3}$ tell you about the trend of the data?
3. How do you convert $y = -\frac{5}{3}x + \frac{38}{3}$ to standard form $Ax + By = C$?
4. What is the y-intercept of this line, and how can it be interpreted in this context?
5. How would the equation change if one of the points were moved vertically by 2 units?

Tip:

When calculating slopes, always verify the subtraction order (y-coordinates first, then x-coordinates) to avoid sign errors.