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 $(3,1)$ and $(8,9)$.

Step2: Calculate the slope $m$

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Substitute $(x_1,y_1)=(3,1)$ and $(x_2,y_2)=(8,9)$ into the formula: $m=\frac{9 - 1}{8 - 3}=\frac{8}{5}$.

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

The slope - intercept form is $y=mx + b$. Use the point $(3,1)$ and $m = \frac{8}{5}$. Substitute into the equation: $1=\frac{8}{5}\times3 + b$. Then $1=\frac{24}{5}+b$. Solve for $b$: $b=1-\frac{24}{5}=\frac{5 - 24}{5}=-\frac{19}{5}$.

Step4: Write the equation of the line

The equation of the line in slope - intercept form is $y=\frac{8}{5}x-\frac{19}{5}$.

Answer:

$y=\frac{8}{5}x-\frac{19}{5}$