Question

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

Explanation:

Step1: Find two points on the trend - line

Let's take the points (4, 2) and (7, 9).

Step2: Calculate the slope $m$

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Substituting $x_1 = 4,y_1 = 2,x_2 = 7,y_2 = 9$ gives $m=\frac{9 - 2}{7 - 4}=\frac{7}{3}$.

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 $(4,2)$ and $m=\frac{7}{3}$, we have $y - 2=\frac{7}{3}(x - 4)$. Expanding gives $y-2=\frac{7}{3}x-\frac{28}{3}$. Then $y=\frac{7}{3}x-\frac{28}{3}+2=\frac{7}{3}x-\frac{28 - 6}{3}=\frac{7}{3}x-\frac{22}{3}$.

Answer:

$y=\frac{7}{3}x-\frac{22}{3}$