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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=−14x+9
y equals negative Start Fraction 1 over 4 End Fraction x plus 9

y=−58x+9
y equals negative Start Fraction 5 over 8 End Fraction x plus 9

y=−14x
y equals negative Start Fraction 1 over 4 End Fraction x

y=1x+9
y equals 1 x plus 9
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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 \( b \).

From the points provided:

• The line passes approximately through the points (0, 9) and (10, 6.5).

1. Finding the slope (m): The slope \( m \) is calculated using the formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Using the points (0, 9) and (10, 6.5): \[ m = \frac{6.5 - 9}{10 - 0} = \frac{-2.5}{10} = -0.25 \]

2. Finding the y-intercept (b): Since we know the line passes through (0, 9), we can see that the y-intercept \( b \) is 9.

3. Writing the equation: Substitute \( m \) and \( b \) into the slope-intercept form: \[ y = -0.25x + 9 \]

In fraction form, \( -0.25 = -\frac{1}{4} \), so the equation can be written as: \[ y = -\frac{1}{4}x + 9 \]

Thus, the correct response is: y = -\frac{1}{4}x + 9.