Answer:
The slope of the perpendicular line is -2.
Explanation:
A perpendicular line has a slope that is the negative inverse of the slope of the reference line. The reference line in this problem is 3x-6y=144.
Let's rearrange this equation to standard slope-intercept form of y=mx+b, where m is the slope and b is the y-intercept (the valuue of y when x=0).
3x-6y=144
-6y=144-3x
-6y=-3x + 144
y = (3/6)x + (144/-6)
y = (1/2)x - 24
This line has a slope of (1/2) and a y-intercept of -24. A line perpendicular to this will have a slope that is the negative inverse of (1/2). This would be -2. The new line will take form:
y = -2x + b
We are not given b, and there is not enough information to calculate one, so let's assume a value of -24, so that it intersects the original line at (0, -24). See the attached graph.