Line a is represented by the equation y=14x+8 . 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=14x+1y=4x−8y=−4x−3

y=1/4x+1 is parallel to line a; y=4x−8 is neither parallel nor perpendicular to line a; y=−4x−3 is perpendicular to line a.

Step-by-step explanation:

Two lines that are parallel have the same slope.

Line a is written in slope-intercept form, y=mx+b, where m is the slope and b is the y-intercept.  In line a, the value of m is 1/4; this means the slope is 1/4.

The slope of the first line, y=1/4x+1, is 1/4.  Since the slopes are the same, the lines are parallel.

None of the other lines have a slope of 1/4, so none of the others are parallel to line a.

Two lines that are perpendicular have slopes that are negative reciprocals; this means their signs are opposite and the fractions representing the slopes are "flipped."  Since the slope of line a = 1/4, any line perpendicular to it will have a slope of -4/1, or -4.  The only line with a slope of -4 is the last one, y=-4x-3.  This is perpendicular to line a.

The remaining line, y=4x-8, is neither perpendicular nor parallel to line a.

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