Question

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Answer 1

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`\displaystyle Perpendicular`

Explanation:

Convert each equation to Slope-Intercept Form:

`\displaystyle 3y - 6x - 7 = 0 → 3y - 6x = 7 → 3y = 6x + 7 → y = 2x + 2(1)/(3) \\ \\ 2y + x = 3 → 2y = -x + 3 → y = -(1)/(2)x + 1(1)/(2)`

Take a look at
`\displaystyle 2` and
`\displaystyle -(1)/(2).` 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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