Final answer:
The two lines y=-2x+1 and x+2y=7 are neither parallel nor perpendicular as their slopes are -2 and -½ respectively, which are not equal nor negative reciprocals of each other.
Step-by-step explanation:
To determine whether the two lines y=-2x+1 and x+2y=7 are parallel, perpendicular, or neither, we first need the lines in slope-intercept form, which is y = mx + b, where 'm' represents the slope and 'b' represents the y-intercept.
The first line is already in this form with a slope of -2. The second equation can be rewritten as y = -½x + ⅓½. The slope of the second line is -½. For two lines to be parallel, their slopes must be identical; for two lines to be perpendicular, the product of their slopes must be -1.
Here, since neither condition is met (the slopes are different but their product is not -1), we can conclude that the two lines are neither parallel nor perpendicular.
The answer to our question "Are the two lines y=-2x+1 and x+2y=7 parallel, perpendicular, or neither?" is c) Neither.