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

Given that the equation of line a is given by y = -2x + 3.

For parallel lines, the slopes are equal, thus the equation of a line parallel to line a will be given by y = -2x + c where c is an arbitrary constant.

For perpendicular lines, the slope of the second line is given by $m_2=- \frac{1}{m_1}$, thus the slope of the line perpendicular to line a is $-\frac{1}{-2} = \frac{1}{2}$ and the equation of the line is given by $y= \frac{1}{2} x+c$, where c is an arbitrary constant.


Therefore, for the given equations:

y = 2x - 1 is neither parallel nor perpendicular to line a.

y = -2x + 5 is parallel to line a

$y= \frac{1}{2} x+7$ is perpendicular to line a.