Final answer:
The slope of all lines perpendicular to the line 3x - 4y = 24 is -4/3, which means that the correct answer is option A.
Step-by-step explanation:
The question asks what is the slope of all lines perpendicular to a given line. The given line is 3x - 4y = 24. To find the slope of lines perpendicular to this, we first need to determine the slope of the given line. The slope-intercept form of a line is y = mx + b, where m is the slope. By rearranging the given equation to this form, we get:
y = (3/4)x - 6
Now, we can see that the slope (m) of this line is 3/4. Lines that are perpendicular have slopes that are negative reciprocals of each other. The negative reciprocal of 3/4 is -4/3. Therefore, the slope of all lines perpendicular to 3x - 4y = 24 is -4/3. This corresponds to option A.