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 - point coordinates

The two yellow points are $(2,1)$ and $(8,8)$.

Step2: Calculate the slope $m$

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Substitute $(x_1,y_1)=(2,1)$ and $(x_2,y_2)=(8,8)$ into it.
$m=\frac{8 - 1}{8 - 2}=\frac{7}{6}$

Step3: Use the point - slope form to find the y - intercept $b$

The slope - intercept form is $y=mx + b$. Use the point $(2,1)$ and $m = \frac{7}{6}$.
$1=\frac{7}{6}\times2 + b$
$1=\frac{7}{3}+b$
$b=1-\frac{7}{3}=\frac{3 - 7}{3}=-\frac{4}{3}$

Step4: Write the equation of the line

Substitute $m=\frac{7}{6}$ and $b =-\frac{4}{3}$ into $y=mx + b$.
$y=\frac{7}{6}x-\frac{4}{3}$

Answer:

$y=\frac{7}{6}x-\frac{4}{3}$