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. From the graph, we can take the points (10, 10) and (60, 60).

Step2: Calculate the slope $m$

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Substituting $x_1 = 10,y_1 = 10,x_2 = 60,y_2 = 60$ into the formula, we get $m=\frac{60 - 10}{60 - 10}=1$.

Step3: Find the y - intercept $b$

We use the point - slope form of a line $y - y_1=m(x - x_1)$ and then convert it to the slope - intercept form $y=mx + b$. Using the point (10, 10) and $m = 1$, we have $y-10=1\times(x - 10)$. Simplifying gives $y-10=x - 10$, so $y=x$.

Answer:

$y=x$