Parallel lines have the same slope.
Coincide lines have the same equation.
Intersect lines have different slope.
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6x - 4y = 24, 3y + 2x = 12 - different equation (not coincide)
[tex]6x-4y=24\qquad\text{subtract 6x from both sides}\\\\-4y=-6x+24\qquad\text{divide both sides by (-4)}\\\\y=\dfrac{-6}{-4}x+\dfrac{24}{-4}\\\\y=\dfrac{3}{2}x-6\to slope=\dfrac{3}{2}\\------------------------\\3y+2x=12\qquad\text{subtract 2x from both sides}\\\\3y=-2x+12\qquad\text{divide both sides by 3}\\\\y=\dfrac{-2}{3}x+\dfrac{12}{3}\\\\y=-\dfrac{2}{3}x+4\to slope=-\dfrac{2}{3}[/tex]
The lines have different slope, therefore are intersect.
