Use the image to answer the question.

Question

An illustration of a scatterplot graph shows x-axis ranging from 0 to 10 in increments of 1 and y-axis ranging from 0 to 10 in increments of 1. Multiple points are plotted around a line that points downward to the right with an arrowhead on the bottom.
The line passes approximately through left parenthesis 0 comma 9 right parenthesis, left parenthesis 4 comma 8 right parenthesis, left parenthesis 8 comma 7 right parenthesis, and left parenthesis 10 comma 6.5 right parenthesis. 12 points are plotted close to the line.

Write an equation in slope-intercept form of the trend line.

(1 point)
Responses

y = − 5/8x + 9

y = 1x +9

y = −1/4x + 9

y = −1/4x

Answer 1

To find the equation of the trend line in slope-intercept form (y = mx + b), we need to determine the slope (m) and the y-intercept (b) of the line.

From the points provided, we see that the line passes through the approximate points (0, 9) and (10, 6.5).

1. Calculate the slope (m): The formula for slope (m) is: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Using the points (0, 9) and (10, 6.5): \[ m = \frac{6.5 - 9}{10 - 0} = \frac{-2.5}{10} = -\frac{1}{4} \]

2. Determine the y-intercept (b): Since the line passes through the point (0, 9), the y-intercept (when x = 0) is clearly: \[ b = 9 \]

3. Write the equation: Using the slope and the y-intercept, we can write the equation in slope-intercept form: \[ y = -\frac{1}{4}x + 9 \]

Thus, the correct answer from the options given is: y = −1/4x + 9.