Answer: Given a line represented by the equation 3x + y = 9, the slope of the line is -3/1. Since we know that the slope of the line perpendicular to this line is the negative reciprocal of the original line's slope, we can find the slope of the perpendicular line by taking -1/-3 = 1/3.
To find the equation of the perpendicular line that passes through the point (1,-2), we can use the point-slope form of the line equation, which is: y - y1 = m(x - x1) where m is the slope of the line and (x1,y1) is a point on the line.
Therefore, the equation of the perpendicular line that passes through the point (1,-2) is:
y - (-2) = (1/3)(x - 1)
y + 2 = (1/3)x + (1/3)
y = (1/3)x - (2/3)
So the final equation of the perpendicular line is y = (1/3)x - (2/3)
Explanation: