Question

Determine if the given lines are parallel, perpendicular, or neither.

-2x-3y=9

4x+6y=24

Answer 1

The lines are parallel.

Explanation:

Given the lines

`-2x-3y=9`

`4x+6y=24`

Writing the equations in the slope-intercept form

`y=mx+b`

where m is the slope and b is the y-intercept

`-2x-3y=9`

`y=-(2)/(3)x-3`

Thus, the slope = m₁ = -2/3

also

`4x+6y=24`

• 
  `y=-(2)/(3)x+4`

Thus, the slope = m₂ = -2/3

• We know that parallel lines have equal slopes

As

m₁ = m₂

Thus, the lines are parallel.