Answer:
y=−1/3x−10 is perpendicular to line a; y=1/3x+1 is neither parallel nor perpendicular to line a; and y=3x−2 is parallel to line a.
Step-by-step explanation:
Two lines are parallel if they have the same slope. These equations are all written in slope-intercept form, y=mx+b, where m is the slope and b is the y-intercept.
The slope of line a, m, is 3.
The only of our three equations with a slope of 3 is y=3x-2. This one is parallel to line a.
Two lines are perpendicular if their slopes are negative reciprocals; this means the slopes are opposite signs and flipped. Since the slope of line a is 3, which is the same as 3/1, if a line is perpendicular to a the slope must be -1/3 (flipped and opposite signs).
The only line with a slope of -1/3 is the first one, y=-1/3x-10.
The middle equation, y=1/3x+1, is not parallel to line a, since the slope is not a. This equation is not perpendicular to line a since the slope is 1/3; this is a reciprocal but is not the opposite sign. It is neither parallel nor perpendicular.
