For this case we have by definition, that if two lines are parallel then their slopes are equal.
We manipulate the equations algebraically to take them to the form y = mx + b.
Equation 1:
[tex]2y = -3x + 8\\y = - \frac {3} {2} x + 4[/tex]
Thus, the slope of this line is [tex]- \frac {3} {2}.[/tex]
Equation 2:
[tex]6x + 2y = 9\\2y = 9-6x\\2y = -6x + 9\\y = \frac {-6x + 9} {2}\\y = -3x + \frac {9} {2}[/tex]
The slope of this line is -3.
As the slopes are not equal, then the lines are not parallel.
Answer:
False
