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

Sep 21, 2016

No they are not parallel.

#### Explanation:

Manipulate both so that they are in the form $y = m x + c$

Where $m$ is the gradient.

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Consider $2 y = 3 x + 4$

Divide both sides by 2

$\frac{2}{2} \times y = \frac{3}{2} x + \frac{4}{2} \text{ "->" } y = \frac{3}{2} x + 2$
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Consider $- 3 x - 2 y = 8$

Multiply both sides by $\left(- 1\right)$

$+ 3 x + 2 y = - 8$

Subtract $3 x$ from both sides

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

$2 y = - 3 x - 8$

Divide both sides by 2

$y = - \frac{3}{2} x - 4$
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In one case the gradient is $+ \frac{3}{2}$
In the other case the gradient is $- \frac{3}{2}$

As the gradients are different they are NOT parallel