Use the image to answer the question.

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=5.67x+8
y equals 5.67 x plus 8

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

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

y=1/5x+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 y-intercept \(b\).

Based on the points given, we can see that as \(x\) increases, \(y\) decreases. The points provided seem to decrease as \(x\) increases. Here are two points we can use to calculate the slope:

Let's take the points \( (0, 8) \) and \( (40, 0) \):

• When \(x = 0\), \(y = 8\)
• When \(x = 40\), \(y = 0\)

Now we can calculate the slope \(m\): \[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{0 - 8}{40 - 0} = \frac{-8}{40} = -\frac{1}{5} \]

Now, we need to determine the y-intercept \(b\). From the point \( (0, 8) \), we see that when \(x = 0\), \(y = 8\). Therefore, the y-intercept \(b\) is 8.

Putting the slope and y-intercept together, we get the equation of the line: \[ y = -\frac{1}{5}x + 8 \]

So, the equation in slope-intercept form is: y = -1/5x + 8.

Thus, the correct response from your options is: y=−1/5x+8.