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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+40
y equals negative 2 x plus 40

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

1 answer

To determine the equation of the trend line from the scatterplot described, we first need to identify the slope and intercept of the line.

Based on the points mentioned, we can observe the following:

  • The line passes through the point (0, 40), indicating that the y-intercept (b) is 40 when x is 0.
  • The trend line appears to decrease at a steady rate as x increases.

From the given points, we can calculate the slope (m) using any two points. For instance, let’s take the points (0, 40) and (2, 36):

The formula for slope (m) is: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \]

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

  • \( y_2 = 36 \) (at x = 2)
  • \( y_1 = 40 \) (at x = 0)
  • \( x_2 = 2 \)
  • \( x_1 = 0 \)

Now, substituting the values: \[ m = \frac{36 - 40}{2 - 0} = \frac{-4}{2} = -2 \]

Thus, the slope is -2.

Now we can write the equation in slope-intercept form \( y = mx + b \): \[ y = -2x + 40 \]

Therefore, the correct equation of the trend line is: y = −2x + 40.