Answer:
3x - y - 2 = 0
Explanation:
The line-3x - 9y - 12 is given in the general form of the equation of a line, Ax + By + C = 0, where A = -3, B = -9, and C = -12.
To find the equation of the line that passes through the point (2, -8) and is perpendicular to the line-3x - 9y - 12, we need to find the slope of the perpendicular line. The slope of a line perpendicular to another line is the negative reciprocal of the slope of the original line.
The slope of the line-3x - 9y - 12 can be found using the slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept. Rearranging the general form equation:
-3x - 9y - 12 = 0
9y = 3x + 12
y = (3/9)x + 4
The slope of the line is m = 3/9. To find the slope of the perpendicular line, we find the negative reciprocal:
m_perpendicular = -1 / (3/9) = -9 / 3
We have the slope of the perpendicular line, now we need to find its equation. To do this, we use the point-slope form of the equation of a line:
y - y1 = m(x - x1)
where (x1, y1) is the point through which the line passes and m is the slope of the line. Plugging in the values for the point (2, -8) and the slope -9/3:
y - (-8) = -9/3 (x - 2)
y + 8 = -3x + 6
3x - y - 2 = 0