Question

what is the equation of the trend line in the scatter plot? use the two orange 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 orange points seem to be approximately $(3,3)$ and $(8,9)$.

Step2: Calculate the slope $m$

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Substituting $(x_1,y_1)=(3,3)$ and $(x_2,y_2)=(8,9)$ gives $m=\frac{9 - 3}{8 - 3}=\frac{6}{5}$.

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

The point - slope form is $y - y_1=m(x - x_1)$. Using the point $(3,3)$ and $m = \frac{6}{5}$, we have $y-3=\frac{6}{5}(x - 3)$. Expand it: $y-3=\frac{6}{5}x-\frac{18}{5}$. Then $y=\frac{6}{5}x-\frac{18}{5}+3$. Simplify the constant term: $y=\frac{6}{5}x-\frac{18}{5}+\frac{15}{5}=\frac{6}{5}x-\frac{3}{5}$.

Answer:

$y=\frac{6}{5}x-\frac{3}{5}$