Question

what is the equation of the trend line in the scatter plot?

Explanation:

Step1: Find two points on the trend - line

We can choose the points (2, 2) and (8, 8).

Step2: Calculate the slope $m$

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Substituting $(x_1,y_1)=(2,2)$ and $(x_2,y_2)=(8,8)$ gives $m=\frac{8 - 2}{8 - 2}=\frac{6}{6}=1$.

Step3: Find the y - intercept $b$

Using the point - slope form $y - y_1=m(x - x_1)$ with the point $(2,2)$ and $m = 1$, we have $y-2=1\times(x - 2)$. Simplifying gives $y-2=x - 2$, so $y=x$.

Answer:

$y = x$