Final answer:
The slope of a line perpendicular to the line with the equation 6x - 4y = 30 is -2/3, which is the negative reciprocal of the original line's slope, 3/2.
Step-by-step explanation:
To determine the slope of a line perpendicular to the given line 6x - 4y = 30, we first need to express the given line in slope-intercept form, y = mx + b, where m represents the slope and b represents the y-intercept.
First, we solve for y:
6x - 4y = 30
-4y = -6x + 30
y = (6x/4) - (30/4)
y = (3/2)x - 15/2
Here, the slope m of the given line is 3/2. The slope of a line perpendicular to another is the negative reciprocal of the original line's slope. So, if the slope of the original line is 3/2, the slope of the perpendicular line would be -2/3. Therefore, the slope of a line perpendicular to the line with the equation 6x-4y=30 is -2/3.