Final answer:
The slope of the line perpendicular to 4x - 6y = -24 is -3/2.
Step-by-step explanation:
The equation of the given line is 4x - 6y = -24. To find the slope of a line perpendicular to this line, we need to find the slope of the given line first. We can rearrange the equation into the slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept.
4x - 6y = -24
-6y = -4x - 24
y = (4/6)x + 4
So, the slope of the given line is 4/6 or 2/3.
The slope of a line perpendicular to another line is the negative reciprocal of the slope of the given line. So, the slope of the line perpendicular to 4/6 is -3/2.