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. Â 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. Â 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. Â 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. Â This equation is not perpendicular to line a since the slope is 1/3; this is a reciprocal but is not the opposite sign. Â It is neither parallel nor perpendicular.
Parallel lines are those lines which are never intersect to each other.
Perpendicular lines are those lines which are intersect at right angles.
Line [tex]y = 3x - 4[/tex] and [tex]y = 3x - 2[/tex] are parallel.
Line [tex]y = 3x - 2[/tex] and [tex]y=-1/3 x-10[/tex] are perpendicular to each other.
Line [tex]y = 3x - 4[/tex]and [tex]y=1/3x+1[/tex] are neither parallel nor perpendicular.
Parallel lines have always same slope.
Since, Line [tex]y = 3x - 4[/tex] and y = 3x - 2 Â have same slope. therefore these are parallel lines.
Product of slope of perpendicular lines will be always - 1.
Since, product of slope of Line y = 3x - 4 and y=−1/3x−10 are - 1. Therefore, these are perpendicular lines.
Line y = 3x - 4 and y=1/3x+1 are not satisfying parallel lines or perpendicular lines properties. Therefore, these are neither parallel nor perpendicular.
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