Final answer:
The slope of a line parallel to the given line -4x-6y=-8 is 2/3. The slope of a line perpendicular to the given line is -3/2.
Step-by-step explanation:
To determine the slope of a line that is parallel or perpendicular to the given line -4x-6y=-8, we first need to write this line in slope-intercept form (y=mx+b), where m represents the slope and b represents the y-intercept. We do this to find the slope of the original line.
First, rewrite the equation as 6y = 4x - 8 and then divide by 6 to solve for y: y = 2/3x - 4/3. The slope of this line is 2/3. A line parallel to this one will have the same slope, so the slope of the parallel line is also 2/3.
To find the slope of a line perpendicular to the original line, we take the negative reciprocal of the original slope. The negative reciprocal of 2/3 is -3/2. Therefore, the slope of the line perpendicular to the given line is -3/2.