Determine whether each pair of lines are parallel, perpendicular, or neither.

Question

Can you please assist me with help on this with steps to determine weather the lines are parallel, perpendicular, or neither.  

 

 

a. 6x=5y+1 and -12x+10y=1



b. 6+4x=3y and 3x+4y=8

Answer 1

If 2 lines are parallel, they have the same slope.  If they are perpendicular, the product of their slopes is -1. 

 

(a)

 

(i)  6x=5y+1 ⇒ y = (6/5)x - 1/5

 

(ii) -12x+10y=1 ⇒ y = (12/10)x + 1/10 = (6/5)x + 1/10

 

Slope of line (i) is 6/5

Slope of line (ii) is 6/5

 

Lines (i) and (ii) are parallel

 

(b)

 

(i)  6+4x=3y ⇒ y = (4/3)x + 2

(ii) 3x+4y=8 ⇒ y = (-3/4)x + 2

 

Slope of line (i) is 4/3

Slope of line (ii) is -3/4

 

(4/3)(-3/4) = -1

 

Lines (i) and (ii) are perpendicular.