Use the image to answer the question.

Question

An illustration of a scatterplot graph is titled Price versus Units Sold. It shows x-axis, labeled as units sold in hundreds, ranging from 0 to 13 in increments of 1 and y-axis, labeled as price in dollars, ranging from 0 to 44 in increments of 4.
Multiple points are plotted around a line that points downward to the right with an arrowhead on the bottom. The line passes through the approximate points: left parenthesis 0 comma 40 right parenthesis, left parenthesis 2 comma 36 right parenthesis, left parenthesis 4 comma 32 right parenthesis, left parenthesis 6 comma 28 right parenthesis, left parenthesis 8 comma 24 right parenthesis, left parenthesis 10 comma 20 right parenthesis, and left parenthesis 13 comma 14 right parenthesis. 29 points are plotted close to the line.

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

(1 point)
Responses

y=−2x+40
y equals negative 2 x plus 40

y=2x+40
y equals 2 x plus 40

y=−2x+24
y equals negative 2 x plus 24

y=−4/3x+40

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 you provided, we can calculate the slope \(m\) using two points. Let's take the points \((0, 40)\) and \((10, 20)\):

1. Calculate the slope \(m\): \[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{20 - 40}{10 - 0} = \frac{-20}{10} = -2 \]

2. Use the slope-intercept form: Now, we can find the equation using one of the points. Let's use the point \((0, 40)\): \[ y = -2x + b \] When \(x = 0\), \(y = 40\): \[ 40 = -2(0) + b \implies b = 40 \]

So, the equation of the trend line is: \[ y = -2x + 40 \]

Thus, the correct response is: y = −2x + 40.