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

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

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

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

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

From the information given, the line passes through the points \( (0, 9) \) and \( (4, 8) \):

  1. Find the slope (m): The formula for the slope \( m \) is: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Taking points \( (0, 9) \) and \( (4, 8) \): \[ m = \frac{8 - 9}{4 - 0} = \frac{-1}{4} \]

  2. Find the y-intercept (b): The y-intercept is the value of \( y \) when \( x = 0 \). From the point \( (0, 9) \), we immediately see that \( b = 9 \).

  3. Write the equation: Now, we can substitute the values of \( m \) and \( b \) into the slope-intercept form: \[ y = -\frac{1}{4}x + 9 \]

Thus, the correct response is:

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