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.

Question

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+8
y equals 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

Answer 1

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) from the points mentioned.

From the points provided on the line:

• The line roughly passes through (0, 8) and (40, 0).

To calculate the slope (m), we can use the slope formula:

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

Choosing the points (0, 8) and (40, 0):

• Let \( (x_1, y_1) = (0, 8) \) and \( (x_2, y_2) = (40, 0) \).

Substituting the values into the slope formula:

\[ m = \frac{0 - 8}{40 - 0} = \frac{-8}{40} = -\frac{1}{5} \]

Next, we use the y-intercept (b). The line passes through the point (0, 8), which gives us:

\[ b = 8 \]

Now we can write the equation of the trend line:

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

Thus, the correct response is:

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