Question

Bivariate Data Analysis & Probability Online Practice
Complete this assessment to review what you've learned. It will not count toward your grade.
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Question
Use the image to answer the 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=−43x+40
y equals negative Start Fraction 4 over 3 End Fraction x plus 40

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

y=−2x+24

Answer 1

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

From the information given:
- The line seems to pass through the points (0, 40) and (10, 20):
- At (0, 40), when units sold is 0, the price is $40.
- At (10, 20), when units sold is 10 (or 1000 units), the price is $20.

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

Now that you have the slope, next identify the y-intercept (b). The y-intercept is the value of y when x = 0. From the point (0, 40), you know that when units sold is zero, the price is $40. Therefore, the y-intercept (b) = 40.

Now, substituting the values for m and b into the slope-intercept form yields:
\[
y = -2x + 40
\]

So the equation of the trend line is:
**y = -2x + 40**

The correct response is:
**y = -2x + 40**.