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

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

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

y=−15x+3

Answer 1

To find the equation of the trend line, we need to determine the slope (m) and the y-intercept (b) of the line.

From the points you provided, we can observe that:

• The line passes through (0, 8). This gives us the y-intercept (b = 8).
• The line passes through several other points, but we can also choose any two points to calculate the slope. For example, we can use (0, 8) and (20, 4) to find the slope.

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

Choosing the points (0, 8) and (20, 4):

\[ m = \frac{4 - 8}{20 - 0} = \frac{-4}{20} = -\frac{1}{5} \]

Now we can write the equation in slope-intercept form, which is:

\[ y = mx + b \]

Substituting the values we found:

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

So, the equation of the trend line is:

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