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 - yellow points

Let the two yellow points be $(x_1,y_1)=(30,70)$ and $(x_2,y_2)=(90,25)$.

Step2: Calculate the slope $m$

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. So, $m=\frac{25 - 70}{90 - 30}=\frac{-45}{60}=-\frac{3}{4}$.

Step3: Use the slope - intercept form $y=mx + b$ to find $b$

Substitute $m =-\frac{3}{4}$ and the point $(x_1,y_1)=(30,70)$ into $y=mx + b$. We get $70=-\frac{3}{4}\times30 + b$. Then $70=-\frac{90}{4}+b$. Solving for $b$: $b = 70+\frac{90}{4}=\frac{280 + 90}{4}=\frac{370}{4}=\frac{185}{2}$.

Answer:

$y =-\frac{3}{4}x+\frac{185}{2}$