Question

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Trend Lines Quick Check
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Question
Use the image to answer the 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=−58x+9
y equals negative Start Fraction 5 over 8 End Fraction 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

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

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, let's calculate the slope (m) using two of the points that the line passes through. We can use the points (0, 9) and (8, 7):

1. **Calculate the slope (m)**:
\[
m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{7 - 9}{8 - 0} = \frac{-2}{8} = -\frac{1}{4}
\]

2. **Determine the y-intercept (b)**:
Since one of the points is (0, 9), the y-intercept (b) is the y-coordinate of this point, which is 9.

Now we can plug the values of m and b into the slope-intercept form:
\[
y = -\frac{1}{4}x + 9
\]

Among the provided options, the correct equation for the trend line is:
**y = -Start Fraction 1 over 4 End Fraction x + 9** or:
**y = -\frac{1}{4}x + 9**.