Final answer:
To find a line perpendicular to another, we look for the negative reciprocal of its slope. Assuming that line MN has a slope of 2, the line with a slope of -1/2 (option c) would be perpendicular.
Step-by-step explanation:
To find a line that is perpendicular to line MN, we must identify the slope of line MN and then determine the slope that would be perpendicular to it. The equation of a line in the form y = mx + b gives us a straight line where m represents the slope of the line, and b represents the y-intercept.
If line MN is perpendicular to one of the options given, the slope of the perpendicular line must be the negative reciprocal of the slope of line MN. Since no slope for MN was given, we're assuming the slope of MN to be 1 for finding a perpendicular line.
Therefore, the negative reciprocal of the slope of line MN (1) would be -1. So, we are looking for an equation with a slope of -1. This directs us to the equation y = -1/2x which is option c), as the slope here is -1/2 which is the negative reciprocal of 2, considering that line MN must have a slope of 2 to necessitate a slope of -1/2 for perpendicularity.