Question

what is the equation of the trend line in the scatter plot?
use the two blue points to write the equation in slope - intercept form. write any coefficients as integers, proper fractions, or improper fractions in simplest form.

Explanation:

Step1: Find the coordinates of two blue points

The two blue points are $(2,2)$ and $(7,9)$.

Step2: Calculate the slope $m$

The slope formula is $m = \frac{y_2 - y_1}{x_2 - x_1}$.
Substitute $(x_1,y_1)=(2,2)$ and $(x_2,y_2)=(7,9)$ into the formula:
$m=\frac{9 - 2}{7 - 2}=\frac{7}{5}$.

Step3: Use the point - slope form to find the equation

The point - slope form is $y - y_1=m(x - x_1)$.
Using the point $(2,2)$ and $m = \frac{7}{5}$:
$y - 2=\frac{7}{5}(x - 2)$.

Step4: Simplify to slope - intercept form $y=mx + b$

Expand the right side: $y - 2=\frac{7}{5}x-\frac{14}{5}$.
Add 2 to both sides: $y=\frac{7}{5}x-\frac{14}{5}+2$.
Since $2=\frac{10}{5}$, then $y=\frac{7}{5}x+\frac{- 14 + 10}{5}=\frac{7}{5}x+\frac{6}{5}$.

Answer:

$y=\frac{7}{5}x+\frac{6}{5}$