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 equals negative Start Fraction 5 over 8 End Fraction x plus 9

y=1x+9
y equals 1 x plus 9

y=−1/4x+9
y equals negative Start Fraction 1 over 4 End Fraction x plus 9

y=−1/4x

Answer 1

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

From the points mentioned:

• (0, 9)
• (4, 8)
• (8, 7)
• (10, 6.5)

Let's calculate the slope (m) using two points, for example, (0, 9) and (10, 6.5):

\[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{6.5 - 9}{10 - 0} = \frac{-2.5}{10} = -0.25 \]

Next, we use the slope-intercept form and the y-intercept from the point (0, 9). Since the line passes through (0, 9), the y-intercept (b) is 9.

Putting it all together, we have:

\[ y = -\frac{1}{4}x + 9 \]

Therefore, the correct answer is:

y = −1/4x + 9.