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

Let the two yellow points be $(x_1,y_1)=(4,7)$ and $(x_2,y_2)=(7,2)$.

Step2: Calculate the slope $m$

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Substitute the values: $m=\frac{2 - 7}{7 - 4}=\frac{-5}{3}=-\frac{5}{3}$.

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 $(4,7)$ and $m =-\frac{5}{3}$, we have $y-7=-\frac{5}{3}(x - 4)$. Expand it: $y-7=-\frac{5}{3}x+\frac{20}{3}$. Then $y=-\frac{5}{3}x+\frac{20}{3}+7$. Since $7=\frac{21}{3}$, $y=-\frac{5}{3}x+\frac{20 + 21}{3}=-\frac{5}{3}x+\frac{41}{3}$.

Answer:

$y =-\frac{5}{3}x+\frac{41}{3}$