Question

Line a is represented by the equation y=−2x+3 . 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=2x−1y=−2x+5y=12x+7

Answer 1

To determine if the line is parallel, perpendicular, or neither to the given line, we must compare their slopes.

Given equation:   y = -2x + 3
slope = -2

The equation of the line can be calculated by -a/b of the standard equation. 

(1) y = 2x - 1 ,  slope = 2

Since, this is just the negative of the given line, the lines are neither parallel nor perpendicular. 

(2) y = -2x + 5,  slope = -2

Since the slope is equal to that of the given equation, this line is parallel with the given equation.

(3) y = 12x + 7  ,  slope = 12

Since the slope do not have a special relation to the slope of the given line, it is neither parallel nor perpendicular to the given. 

Answer 2

Answer:

y=2x−1 is neither parallel nor perpendicular to line a; y=−2x+5 is parallel to line a; y=1/2x+7 is perpendicular to line a.

Step-by-step explanation:

Line a is written in slope-intercept form, y=mx+b, where m is the slope and b is the y-intercept.  The slope of line a, the number in place of m, is -2.

Any line parallel to line a will have the same slope as line a, -2.  The only line with this slope is y=-2x+5.

Any line perpendicular to this line will have a slope that is the negative reciprocal (this means the opposite sign and flipped upside down).  This means that the slope of any line that is perpendicular to line a will have a slope of 1/2.  The only line that has a slope of 1/2 is y=1/2x+7.