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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
y equals negative Start Fraction 1 over 4 End Fraction x

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

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

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

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

Looking at the approximate points provided, we can identify two points to calculate the slope. Let's use the points \( (0, 9) \) and \( (10, 6.5) \).

  1. Calculate the slope (m): \[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{6.5 - 9}{10 - 0} = \frac{-2.5}{10} = -0.25 \]

  2. Identify the y-intercept (b): From the point \( (0, 9) \), we can see that when \( x = 0 \), \( y = 9 \). So, the y-intercept \( b \) is 9.

  3. Write the equation: Now we can substitute the slope and y-intercept into the slope-intercept form: \[ y = -0.25x + 9 \]

Converting this to fraction format (since -0.25 = -\(\frac{1}{4}\)): \[ y = -\frac{1}{4}x + 9 \]

Based on the options given, the correct response is: y equals negative Start Fraction 1 over 4 End Fraction x plus 9.