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Trend Lines Quick Check

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Question
Use the image to answer the question.

A scatterplot graph shows x-axis ranging from 0 to 50 and y-axis ranging from 0 to 10. Multiple points are plotted around a line that points downward to the right with an arrowhead on the bottom.
The x-axis is drawn in increments of 5 but labeled in increments of 10. The y-axis is drawn in increments of 1 but labeled in increments of 2. The line passes approximately through left parenthesis 0 comma 8 right parenthesis, left parenthesis 10 comma 6 right parenthesis, left parenthesis 15 comma 5 right parenthesis, left parenthesis 20 comma 4 right parenthesis, left parenthesis 25 comma three right parenthesis, and left parenthesis 40 comma 0 right parenthesis. 14 points are plotted close to or on the line.

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

(1 point)
Responses

y=−15x+3
y equals negative Start Fraction 1 over 5 End Fraction x plus 3

y=5.67x+8
y equals 5.67 x plus 8

y=−15x+8
y equals negative Start Fraction 1 over 5 End Fraction x plus 8

y=15x+8
y equals Start Fraction 1 over 5 End Fraction x plus 8

1 answer

To find the equation of the trend line in slope-intercept form (y = mx + b), you need to determine the slope (m) and the y-intercept (b) based on the points provided in the scatterplot.

  1. Identify Points for Calculation: You can use two points from the trend line:

    • Point A: (0, 8)
    • Point B: (10, 6)

  2. Calculate the Slope (m): \[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{6 - 8}{10 - 0} = \frac{-2}{10} = -\frac{1}{5} \]

  3. Find the Y-Intercept (b): The y-intercept is the value of y when x = 0. From point A (0, 8), we can see that: \[ b = 8 \]

  4. Form the Equation: Now substitute the values of slope (m) and y-intercept (b) into the slope-intercept form: \[ y = -\frac{1}{5}x + 8 \]

Based on the options provided, the correct response is: y equals negative Start Fraction 1 over 5 End Fraction x plus 8.