Question

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

Explanation:

Step1: Identify two points on trend - line

Let's take two points on the trend - line: $(4,2)$ and $(9,8)$.

Step2: Calculate the slope $m$

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Substituting $(x_1,y_1)=(4,2)$ and $(x_2,y_2)=(9,8)$ gives $m=\frac{8 - 2}{9 - 4}=\frac{6}{5}=1.2$.

Step3: Use point - slope form to find the equation

The point - slope form is $y - y_1=m(x - x_1)$. Using the point $(4,2)$ and $m = 1.2$, we have $y-2=1.2(x - 4)$.

Step4: Simplify the equation

Expand the right - hand side: $y-2=1.2x-4.8$. Then add 2 to both sides to get $y = 1.2x-2.8$.

Answer:

$y = 1.2x-2.8$