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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=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=−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
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Answer 1

To derive the slope-intercept form of the trend line from the points provided:

1. Identify two points on the line, for example:

   • Point 1: (0, 9)
   • Point 2: (10, 6.5)

2. Calculate the slope (m) using the formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Substituting the points: \[ m = \frac{6.5 - 9}{10 - 0} = \frac{-2.5}{10} = -0.25 \]

3. Use the slope and one point to write the equation in slope-intercept form (y = mx + b):

   • We can use the point (0, 9) where the y-intercept (b) is 9:
   • Thus, the equation becomes: \[ y = -0.25x + 9 \]

In fraction form, this can be represented as: \[ y = -\frac{1}{4}x + 9 \]

Therefore, the correct response is: y = -1/4 x + 9.