Final answer:
The slope of a line perpendicular to 6x + 4y = 64 is 2/3.
Step-by-step explanation:
The equation of the given line is 6x + 4y = 64. To find the slope of a line perpendicular to this line, we need to first find the slope of the given line. Rearranging the equation in the form y = mx + b, we get 4y = -6x + 64 and then y = -3/2x + 16. The slope of this line is -3/2.
The slope of a line perpendicular to another line is the negative reciprocal of the slope of the given line. Therefore, the slope of the line perpendicular to 6x + 4y = 64 is 2/3.