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 (0, 0) and (6, 6).

Step2: Calculate the slope $m$

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Substituting $(x_1,y_1)=(0,0)$ and $(x_2,y_2)=(6,6)$ gives $m=\frac{6 - 0}{6 - 0}=1$.

Step3: Find the y - intercept $b$

The equation of a line is $y = mx + b$. Using the point - slope form with the point $(0,0)$ and $m = 1$, when $x = 0$ and $y = 0$, we substitute into $y=mx + b$: $0=1\times0 + b$, so $b = 0$.

Step4: Write the equation of the line

The equation of the line is $y=mx + b$. Substituting $m = 1$ and $b = 0$ gives $y=x$.

Answer:

$y = x$