Answer:
○ [tex]\displaystyle Perpendicular[/tex]
Step-by-step explanation:
Convert each equation to Slope-Intercept Form:
[tex]\displaystyle 3y - 6x - 7 = 0 → 3y - 6x = 7 → 3y = 6x + 7 → y = 2x + 2\frac{1}{3} \\ \\ 2y + x = 3 → 2y = -x + 3 → y = -\frac{1}{2}x + 1\frac{1}{2}[/tex]
Take a look at [tex]\displaystyle 2[/tex] and [tex]\displaystyle -\frac{1}{2}.[/tex] Their rate of changes [slopes] have a '2' in common, they are not similar. This tells you that these linear equations are not parallel, but perpendicular, because perpendicular equations have OPPOSITE MULTIPLICATIVE INVERSE RATE OF CHANGES [SLOPES].
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