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: Identify two points

Let the two blue - points be $(x_1,y_1)=(50,50)$ and $(x_2,y_2)=(70,80)$.

Step2: Calculate the slope $m$

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Substitute the values: $m=\frac{80 - 50}{70 - 50}=\frac{30}{20}=\frac{3}{2}$.

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 $(50,50)$ and $m = \frac{3}{2}$, we have $y-50=\frac{3}{2}(x - 50)$. Expand it: $y-50=\frac{3}{2}x-75$. Then, solve for $y$: $y=\frac{3}{2}x-75 + 50$, so $y=\frac{3}{2}x-25$.

Answer:

$y=\frac{3}{2}x - 25$