I need help with algebra homework part 2?

Question

Are the following lines parallel, perpendicular or neither?

2x + 3y = -9 and 4x + 9y = -12

Answer 1

The equations are

2x + 3y = -9............(1)  

4x + 9y = -12..........(2)

First equation we can write in slope-intercept form

2x + 3y = -9

Subtract 2x from each side

2x-2x+3y = -2x-9

3y = -2x-9

Divide each side by 3

3y/3 = -2x/3-9/3

y = (-2/3)x-3

slope m₁ = -2/3

Second equation we can write in slope-intercept form

4x + 9y = -12

Subtract 4x from each side

4x-4x+9y = -4x-12

9y = -4x-12

Divide each side by 9

9y/9 =(-4/9)x-12/9

y = (-4/9)x-12/9

Slope m₂ = -4/9

Slope m₁≠m2 then -2/3≠-4/9

The lines are not parallel perpendicular

Slope m₁×m2 then -2/3*-4/9 = 3/2

The lines are not perpendicular.