Write an equation of the line that passes through the point (i)parallel to the given line,and (ii)perpendicular to the given line.
Point: Line:
A) (i) parallel: (ii) perpendicular:
B) (i) parallel: (ii) perpendicular:
C) (i) parallel: (ii) perpendicular:
D) (i) parallel: (ii) perpendicular:
E) (i)parallel: (ii)perpendicular:

Question

Write an equation of the line that passes through the point (i)parallel to the given line,and (ii)perpendicular to the given line. ​
Point:  Line:  ​
A) (i) parallel: (ii) perpendicular: 
B) (i) parallel: (ii) perpendicular: 
C) (i) parallel: (ii) perpendicular: 
D) (i) parallel: (ii) perpendicular: 
E) (i)parallel: (ii)perpendicular:

Quizplus · Accepted Answer

To find the equation of a line that is parallel to a given line, we use the fact that parallel lines have the same slope. The slope of the given line is -1, so the slope of the parallel line is also -1. 
To find the equation of a line that is perpendicular to a given line, we use the fact that perpendicular lines have negative reciprocal slopes. The slope of the given line is -1, so the slope of the perpendicular line is 1. 
Using these slopes, we can find the equations of the lines passing through the given point: 
(i) parallel: y - 17 = -1(x - 5)  or y = -x + 22 
(ii) perpendicular: y - 17 = 1(x - 5)  or y = x + 12

Among the given answer choices, only choice A has these equations.

Write an Equation of the Line That Passes Through the Point