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

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

1 answer

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) using the points on the line.

From the points mentioned:

  • (0, 8)
  • (10, 6)
  • (15, 5)
  • (20, 4)
  • (25, 3)
  • (40, 0)

Step 1: Calculate the slope (m)

Using the points (0, 8) and (10, 6):

\[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{6 - 8}{10 - 0} = \frac{-2}{10} = -\frac{1}{5} \]

Step 2: Find the y-intercept (b)

From the point (0, 8), we see that when x = 0, y = 8. Therefore, the y-intercept (b) is 8.

Step 3: Write the equation

Now, we can write the equation of the trend line:

\[ y = -\frac{1}{5}x + 8 \]

Thus, the correct answer is:

y equals negative Start Fraction 1 over 5 End Fraction x plus 8.