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

The first yellow point is at \((0, 6)\) (where \(x = 0\), \(y = 6\)) and the second yellow point is at \((8, 4)\) (where \(x = 8\), \(y = 4\)).

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

The formula for slope is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Substituting the points \((0, 6)\) as \((x_1,y_1)\) and \((8, 4)\) as \((x_2,y_2)\), we get:
\(m=\frac{4 - 6}{8 - 0}=\frac{-2}{8}=-\frac{1}{4}\)

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

The y - intercept is the value of \(y\) when \(x = 0\). From the point \((0, 6)\), we can see that when \(x = 0\), \(y = 6\), so \(b = 6\).

Step4: Write the equation in slope - intercept form

The slope - intercept form of a line is \(y=mx + b\). Substituting \(m =-\frac{1}{4}\) and \(b = 6\) into the formula, we get:
\(y=-\frac{1}{4}x + 6\)

Answer:

\(y =-\frac{1}{4}x + 6\)