Ais represented by the equation y=3x−4 . how do these equations compare to line a? drag and drop the equations into the boxes to complete the table. parallel to line a perpendicular to line a neither parallel nor perpendicular to line a y=−1/3x−10 y=1/3x+1 y=3x−2

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.

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