To find the equation of the line that contains the given point (12, 4) and is perpendicular to the given line y = -3x - 9, we can use the slope-intercept form of a line, which is y = mx + b, where m is the slope of the line and b is the y-intercept (the point where the line crosses the y-axis).
We are given that the line we are trying to find is perpendicular to the line y = -3x - 9. This means that the slope of our line is the negative reciprocal of the slope of the given line, which is -(-3) = 3.
Since the point (12, 4) lies on the line, we can use the point-slope formula to find the equation of the line. The point-slope formula is y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope of the line.
Substituting the values into the point-slope formula, we get:
y - 4 = 3(x - 12)
Simplifying, we get:
y = 3x - 36
This is the equation of the line in slope-intercept form. Therefore, the equation of the line that contains the point (12, 4) and is perpendicular to the line y = -3x - 9 is y = 3x - 36.