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 points

The two yellow points are \((0, 8)\) and \((7, 5)\).

Step2: Calculate the slope \(m\)

The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Substituting the points \((x_1,y_1)=(0,8)\) and \((x_2,y_2)=(7,5)\), we get \(m=\frac{5 - 8}{7 - 0}=\frac{-3}{7}\).

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

The slope - intercept form is \(y = mx + b\). The line passes through \((0,8)\), so when \(x = 0\), \(y = 8\). Substituting into \(y=mx + b\), we have \(8=\frac{-3}{7}(0)+b\), so \(b = 8\).

Step4: Write the equation

Substitute \(m=\frac{-3}{7}\) and \(b = 8\) into the slope - intercept form \(y=mx + b\). We get \(y=-\frac{3}{7}x + 8\).

Answer:

\(y = -\frac{3}{7}x+8\)