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Question

An illustration of a scatterplot graph shows x-axis ranging from 0 to 10 in increments of 1 and y-axis ranging from 0 to 10 in increments of 1. Multiple points are plotted around a line that points downward to the right with an arrowhead on the bottom.
The line passes approximately through left parenthesis 0 comma 9 right parenthesis, left parenthesis 4 comma 8 right parenthesis, left parenthesis 8 comma 7 right parenthesis, and left parenthesis 10 comma 6.5 right parenthesis. 12 points are plotted close to the line.

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

(1 point)
Responses

y=−58x+9
y equals negative Start Fraction 5 over 8 End Fraction x plus 9

y=−14x
y equals negative Start Fraction 1 over 4 End Fraction x

y=1x+9
y equals 1 x plus 9

y=−14x+9

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 provided in the description, we can calculate the slope between the points (0, 9) and (10, 6.5).

The formula for calculating the slope \(m\) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is:

\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]

Using the points (0, 9) and (10, 6.5):

\[ m = \frac{6.5 - 9}{10 - 0} = \frac{-2.5}{10} = -0.25 \]

Now that we have the slope \(m = -0.25\), we can use one of the points (we'll use (0, 9)) to determine \(b\).

Since when \(x = 0\), \(y\) is equal to 9, therefore \(b = 9\).

Now we can write the equation:

\[ y = -0.25x + 9 \]

To match this with the provided options, we convert \(-0.25\) to a fraction:

\(-0.25\) is \(-\frac{1}{4}\), so the final equation in slope-intercept form is:

\[ y = -\frac{1}{4}x + 9 \]

Thus, the correct response is:

y = -14x + 9 (interpreting the fraction given in the format of the choices).