Scatter Plots & Data Analysis Online Practice

Question

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Question
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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+24
y equals negative 2 x plus 24

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+40

Answer 1

To determine the equation of the trend line in slope-intercept form (y = mx + b), we first need to identify the slope (m) and the y-intercept (b) based on the points given.

The points that the line passes through are approximately:

• (0, 40)
• (2, 36)
• (4, 32)
• (6, 28)
• (8, 24)
• (10, 20)
• (13, 14)

From these points, we can calculate the slope (m):

Using the points (0, 40) and (2, 36):

\[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{36 - 40}{2 - 0} = \frac{-4}{2} = -2 \]

Now we can use the slope and the y-intercept (the value of y when x = 0, which is 40) to write the equation of the trend line:

\[ y = mx + b \]

Substituting in the values we found:

\[ y = -2x + 40 \]

Therefore, the correct response is:

y = -2x + 40.