Determine whether the pair of lines are parallel, perpendicular, or neither. 6x=5y+5 , -18x+15y=5

Question

6x=5y+5

-18x+15y=5

Answer 1

First line is 6x = 5y+5

Subtract 5 to each side.

6x-5 = 5y+5-5

6x-5 = 5y

Divide by 5 to each side.

(6x-5)/5 = 5y/5

6x/5-5/5 = y

y = (6/5)x-1

Slope of the first line is say m1 = 6/5.

Now the second line is -18x+15y = 5

add 18x to each side.

-18x+18x+15y = 5+18x

15y = 18x+5

Divide by 15 to each side.

15y/15 = (18x+5)/15

y = (18/15)x+5/15

y = (6/5)x+1/3

Slope of the second line say m2 = 6/5

m1 = m2

Given lines slopes are equal.

Given lines are parallel lines.