^{5}/

_{2}x

_{ }+ 3

^{5}/

_{2}

^{12}/

_{5})y = 4

^{12}/

_{5})y = -3x + 4

^{12}/

_{5}

^{12}/

_{5}y = -3x + 4

^{5}/

_{12}

^{5}/

_{4}x +

^{5}/

_{3}

^{5}/

_{4}

^{5}/

_{2}does not equal -

^{5}/

_{4}therefore the line are not parallel

True or False?

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Patrick S. | Conquering MathConquering Math

Thank you for your question Lindsey

If two lines are parallel then they have the same slope.

So the first thing we need to do is put each function into slope intercept form and compare the slopes.

5x + 2y = 6

Subtract 5x to both sides

2y = -5x + 6

divide 2 to each side

y = -^{5}/_{2}x_{ }+ 3

Slope = -^{5}/_{2}

3x - ay = 4

Substitute -12/5 for a

3x - (-^{12}/_{5})y = 4

Subtract 3x to both sides

- (-^{12}/_{5})y = -3x + 4

multiply -1 and -^{12}/_{5}

Multiply through by ^{5}/_{12}

y = -^{5}/_{4}x + ^{5}/_{3}

Slope = -^{5}/_{4}

-^{5}/_{2} does not equal -^{5}/_{4} therefore the line are not parallel

Hi Lindsey;

Both equations are in standard form...

Ax+By=C, neither A nor B equal zero, and A is greater than zero.

The slope is -A/B.

5x + 2y = 6

Slope is -5/2

3x - ay = 4

Slope is -[(3/(-a)]

A negative of a negative is positive. Therefore this is...

3/a

a=-12/5

Let's plug this in, and see if the result is -5/2...

[3/(-12/5)]

Let's flip -12/5 into -5/12, and multiply this by 3...

(3)(-5/12)

-15/12

Both the numerator and denominator are divisible by 3...

-5/4

The two equations do NOT have the same slope.

THE TWO EQUATIONS ARE NOT PARALLEL.

3x - (-12/5)y = 4

Multiply both sides by 5:

15x + 12y = 20

slope = -15/12 = -5/4

slope of 5x + 2y = 6 is -5/2

The slopes are not equal so the lines are not parallel.

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