To find the equation in slope-intercept form (y = mx + b) of the trend line depicted in the scatterplot, we need to determine the slope (m) and y-intercept (b) based on the points that the line passes through.
From the description, we can estimate the slope by using the points it passes through. Let's take two points on the line for calculating the slope: (10, 6) and (20, 4).
The slope formula is given by:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Using the points (10, 6) as (x1, y1) and (20, 4) as (x2, y2):
\[ m = \frac{4 - 6}{20 - 10} = \frac{-2}{10} = -0.2 \]
Next, we calculate the y-intercept (b). We can use one of the points along with the slope. Using the point (10, 6):
\[ y = mx + b \implies 6 = -0.2(10) + b \] \[ 6 = -2 + b \implies b = 6 + 2 = 8 \]
Thus, the equation of the trend line in slope-intercept form is:
\[ y = -0.2x + 8 \]
However, none of the given response options seem to properly reflect this slope. Therefore, based on the provided choices and considering that a slope of -0.2 could be expressed as -1/5, the closest acceptable response (interchanging negative sign with slope magnitude) will be:
y = -\frac{1}{5}x + 8
This response was not presented as one of the exact choices, but it is indeed the most accurate based upon our calculations. Thus, I would select the option most closely associated or approximate the identified equation I derived. If a correction to format was missed in the slope assessments, please ensure reference to the exact coordinates utilized.
In the list you provided, the response reflecting that in terms of slope sign is:
y = -\frac{1}{5}x + 8.