5y = -3x -5 or 5y = -5 -3x or 3y -2x = -1 which two lines are parallel?

Question

Which two lines are parallel?

5y = -3x -5

5y = -5 -3x

3y - 2x = -1

Answer 1

Given lines are 5 y = - 3 x - 5 , 5 y = - 5 - 3 x and 3 y - 2 x =  - 1.

Slope intercept form : y = m x + b where m = slope , b = y - intercept

( i )   5 y = - 3 x - 5.

y = ( - 3 x - 5 ) / 5

y = ( - 3 x ) / 5 - 5 / 5 

y = ( - 3 / 5  ) x - 1 5

Slope  (m) = - 3 / 5 

( ii )  5 y = - 5 - 3 x.

y =  (- 5 - 3 x ) / 5

y =  (- 5  / 5 ) - [ ( 3 x ) / 5 ].

y = - 1 - 3 / 5 ( x )

y = - 3 / 5 ( x ) - 1.

slope = - 3 / 5

( iii )  3 y - 2 x =  - 1.

3 y = - 1 + 2 x

y = ( - 1 + 2 x ) / 3

y = - 1 / 3 +(  2 x / 3 )

y = (  2 x / 3 ) - 1 / 3.

slope = 2 / 3

We know that slopes are equal  so the lines are parallel.

So  5 y = - 3 x - 5 and 5 y = - 5 - 3 x are parallel lines.