Determine whether the pair of lines is parallel, perpendicular, or neither.

Question

Determine whether the pair of lines is parallel, perpendicular, or neither.

 

4/3x+y=4

4x+3y=5

 

Answer 1

First we need to solve for y in both equations. 

 

(4/3)x+y=4

y=4-(4/3)x

 

4x+3y=5

3y=5-4x

y=(5/3)-(4/3)x

 

Two lines will be parallel when their slopes are equal, and two lines will be perpendicular when their slopes are negative reciprocals of each other. 

 

Our slopes for these two equations are the coefficient for the x value. 

-(4/3) and -(4/3)

 

Both slopes are equal so these lines are parallel.