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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=−14x+9
y equals negative Start Fraction 1 over 4 End Fraction x plus 9

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

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

y=−58x+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 y-intercept (b) from the points that the line passes through.

From the description, the line passes through the points (0, 9) and (4, 8). We can use these two points to calculate the slope:

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

Using the points (0, 9) and (4, 8):

• \((x_1, y_1) = (0, 9)\)
• \((x_2, y_2) = (4, 8)\)

Calculating the slope: \[ m = \frac{8 - 9}{4 - 0} = \frac{-1}{4} = -\frac{1}{4} \]

Now we can find the y-intercept (b). Since the line passes through (0, 9), the y-intercept is 9.

Putting it all together, the equation of the trend line is: \[ y = -\frac{1}{4}x + 9 \]

Therefore, the correct response is: y = -\frac{1}{4}x + 9