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 at \((0, 7)\) (when \(x = 0\), \(y = 7\)) and \((8, 5)\) (when \(x = 8\), \(y = 5\)).

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

The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let \((x_1,y_1)=(0,7)\) and \((x_2,y_2)=(8,5)\). Then \(m=\frac{5 - 7}{8 - 0}=\frac{-2}{8}=-\frac{1}{4}\).

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

The slope - intercept form of a line is \(y = mx + b\). We know that when \(x = 0\), \(y = 7\) (from the point \((0,7)\)). Substituting \(x = 0\), \(y = 7\) and \(m=-\frac{1}{4}\) into \(y=mx + b\), we get \(7=-\frac{1}{4}(0)+b\), so \(b = 7\).

Step4: Write the equation

Substitute \(m = -\frac{1}{4}\) and \(b = 7\) into the slope - intercept form \(y=mx + b\). The equation is \(y=-\frac{1}{4}x + 7\).

Answer:

\(y = -\frac{1}{4}x + 7\)