To find the equation of the regression line for the given set of points $(3, 4), (6, 6), (9, 9)$, we use the formula for the line of best fit, also called the least squares regression line:

$y = mx + b$

Where:

• $m$ is the slope of the line.
• $b$ is the y-intercept.

Step 1: Calculate the slope $m$

The formula for the slope is:

$m = \frac{n(\sum xy) - (\sum x)(\sum y)}{n(\sum x^2) - (\sum x)^2}$

Where:

• $n$ is the number of points,
• $\sum xy$ is the sum of the products of the $x$ and $y$ values,
• $\sum x$ is the sum of the $x$ values,
• $\sum y$ is the sum of the $y$ values,
• $\sum x^2$ is the sum of the squares of the $x$ values.

From the points $(3, 4), (6, 6), (9, 9)$:

• $n = 3$
• $\sum x = 3 + 6 + 9 = 18$
• $\sum y = 4 + 6 + 9 = 19$
• (\sum xy = (3)(4) + (6)(6) + (9)(9) = 12+36\