The regression line of two variables is the line that minimizes the error sum of squares.
The SD line passes through the means of the two variables (mean of x, mean of y) and the standard deviation away from their means (mean of x + SD of x, mean of y + SD of y).
The slope of the SD line is (SD of y) / (SD of x).
The slope of the regression line is the slope of the SD line multiplied by the correlation.
The regression passes through the means of the two variables.
Knowing the slope and a point on the regression line (the means of x and y), we can calculate the y intercept. This gives us the equation of the regression line.