Question

Is `2y = 3x + 4` parallel to `-3x-2y=8`?

Answer 1

No they are not parallel.

Explanation:

Manipulate both so that they are in the form `y = mx + c`

Where `m` is the gradient.

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Consider `2y=3x+4`

Divide both sides by 2

`2/2xxy=3/2x+4/2" "->" "y=3/2x+2`
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Consider `-3x-2y=8`

Multiply both sides by `(-1)`

`+3x+2y=-8`

Subtract `3x` from both sides

`3x-3x+2y=-3x-8`

`2y=-3x-8`

Divide both sides by 2

`y=-3/2x-4`
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In one case the gradient is `+3/2`
In the other case the gradient is `-3/2`

As the gradients are different they are NOT parallel