Question

what is the equation of the trend line in the scatter plot?
use the two yellow points to write the equation in slope - intercept form. write any coefficients as integers, proper fractions, or improper fractions in simplest form.

Explanation:

Step1: Identify the two yellow points

From the scatter plot, the two yellow points are \((4, 7)\) and \((9, 2)\).

Step2: Calculate the slope (\(m\))

The formula for slope is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let \((x_1,y_1)=(4,7)\) and \((x_2,y_2)=(9,2)\). Then \(m=\frac{2 - 7}{9 - 4}=\frac{-5}{5}=- 1\).

Step3: Find the y - intercept (\(b\))

Use the slope - intercept form \(y = mx + b\) and one of the points, say \((4,7)\). Substitute \(m=-1\), \(x = 4\), and \(y = 7\) into the equation:
\(7=-1\times4 + b\)
\(7=-4 + b\)
Add 4 to both sides: \(b=7 + 4=11\).

Step4: Write the equation

Using \(m=-1\) and \(b = 11\) in the slope - intercept form \(y=mx + b\), we get \(y=-x + 11\).

Answer:

\(y=-x + 11\)