Question

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

Explanation:

Step1: Identify two points on the trend - line

Let's take two points on the trend - line, say (2, 1) and (6, 8).

Step2: Calculate the slope $m$

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Substituting $x_1 = 2,y_1 = 1,x_2 = 6,y_2 = 8$, we get $m=\frac{8 - 1}{6 - 2}=\frac{7}{4}=1.75$.

Step3: Use the point - slope form $y - y_1=m(x - x_1)$

Using the point $(2,1)$ and $m = 1.75$, we have $y - 1=1.75(x - 2)$.

Step4: Convert to slope - intercept form $y=mx + b$

Expand the point - slope form: $y-1 = 1.75x-3.5$. Then $y=1.75x-3.5 + 1$, so $y = 1.75x-2.5$.

Answer:

$y = 1.75x-2.5$