Final answer:
The line y = -120 is parallel to -2x-3y=12, the line y = 2/(13 is neither parallel nor perpendicular to -2x-3y=12, and the line x = -700 is neither parallel nor perpendicular to -2x-3y=12.
Step-by-step explanation:
The given line is -2x-3y=12. We need to determine if each of the given lines is parallel, perpendicular, or neither to this line.
To determine this, we can compare the slopes of the given lines with the slope of the given line.
If two lines have the same slope, they are parallel. If the slopes are negative reciprocals of each other, they are perpendicular. If the slopes are neither the same nor negative reciprocals, then the lines are neither parallel nor perpendicular.
Let's calculate the slopes of the given lines and compare them with the slope of -2x-3y=12:
a. Slope of -2x-3y=12: -2/(-3) = 2/3
Slope of y = -120: this line is parallel to -2x-3y=12 because it has the same slope of 2/3
Slope of y = 2/(13: this line is neither parallel nor perpendicular to -2x-3y=12 because its slope is not the same as 2/3 and not the negative reciprocal of 2/3.
Slope of x = -700: this line is neither parallel nor perpendicular to -2x-3y=12 because it is a vertical line, and vertical lines have undefined slopes.
Therefore, the line y = -120 is parallel to -2x-3y=12, the line y = 2/(13 is neither parallel nor perpendicular to -2x-3y=12, and the line x = -700 is neither parallel nor perpendicular to -2x-3y=12.