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 \((4, 2)\) and \((7, 8)\).

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

The formula for slope is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Substituting \(x_1 = 4\), \(y_1 = 2\), \(x_2 = 7\), \(y_2 = 8\):
\(m=\frac{8 - 2}{7 - 4}=\frac{6}{3}=2\)

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

Use the slope - intercept form \(y = mx + b\) and one of the points, say \((4, 2)\). Substitute \(m = 2\), \(x = 4\), \(y = 2\) into the equation:
\(2=2\times4 + b\)
\(2 = 8 + b\)
Subtract 8 from both sides: \(b=2 - 8=-6\)

Step4: Write the equation

Using the slope - intercept form \(y=mx + b\) with \(m = 2\) and \(b=-6\), the equation is \(y = 2x-6\)

Answer:

\(y = 2x - 6\)