Question

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Trend Lines Quick Check
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Question
Use the image to answer the question.

A scatterplot graph shows x-axis ranging from 0 to 50 and y-axis ranging from 0 to 10. Multiple points are plotted around a line that points downward to the right with an arrowhead on the bottom.
The x-axis is drawn in increments of 5 but labeled in increments of 10. The y-axis is drawn in increments of 1 but labeled in increments of 2. The line passes approximately through left parenthesis 0 comma 8 right parenthesis, left parenthesis 10 comma 6 right parenthesis, left parenthesis 15 comma 5 right parenthesis, left parenthesis 20 comma 4 right parenthesis, left parenthesis 25 comma three right parenthesis, and left parenthesis 40 comma 0 right parenthesis. 14 points are plotted close to or on the line.

Write an equation in slope-intercept form of the trend line.

(1 point)
Responses

y=−15x+8
y equals negative Start Fraction 1 over 5 End Fraction x plus 8

y=−15x+3
y equals negative Start Fraction 1 over 5 End Fraction x plus 3

y=5.67x+8
y equals 5.67 x plus 8

y=15x+8

Answer 1

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

From the points you've provided, it appears the line has a downward slope. Let's use two of the points to calculate the slope. Taking points \( (0, 8) \) and \( (40, 0) \):

The formula for slope \(m\) is:

\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

Using \( (x_1, y_1) = (0, 8) \) and \( (x_2, y_2) = (40, 0) \):

\[
m = \frac{0 - 8}{40 - 0} = \frac{-8}{40} = -\frac{1}{5}
\]

Next, we need to find the y-intercept \(b\). Using the point \( (0, 8) \), we can see that the y-intercept is \(8\) (since when \(x = 0\), \(y = 8\)).

Thus, the equation of the trend line is:

\[
y = -\frac{1}{5}x + 8
\]

Looking at the choices provided:

- **y equals negative Start Fraction 1 over 5 End Fraction x plus 8** is the correct representation.

So the answer is:

**y = -\frac{1}{5}x + 8**.