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 \((0, 80)\) (when \(x = 0\), \(y = 80\)) and the second yellow point is at \((70, 30)\) (when \(x = 70\), \(y = 30\)).

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

The formula for slope between two points \((x_1, y_1)\) and \((x_2, y_2)\) is \(m=\frac{y_2 - y_1}{x_2 - x_1}\).
Substituting \(x_1 = 0\), \(y_1 = 80\), \(x_2 = 70\), \(y_2 = 30\) into the formula:
\(m=\frac{30 - 80}{70 - 0}=\frac{-50}{70}=-\frac{5}{7}\)

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

The slope - intercept form of a line is \(y = mx + b\). We know that when \(x = 0\), \(y = 80\) (from the point \((0, 80)\)). Substituting \(x = 0\), \(y = 80\) and \(m=-\frac{5}{7}\) into \(y=mx + b\):
\(80=-\frac{5}{7}(0)+b\), so \(b = 80\)

Step4: Write the equation

Substitute \(m = -\frac{5}{7}\) and \(b = 80\) into the slope - intercept form \(y=mx + b\):
\(y=-\frac{5}{7}x + 80\)

Answer:

\(y = -\frac{5}{7}x + 80\)