Question

Write an equation for the line that passes through the given point and is parallel to the graph of the given equation.

Answer 1

Answer:

$\displaystyle 2x - 3y = 6\:OR\:y = \frac{2}{3}x - 2 \\ \\ 3x - 2y = 40\:OR\:y = \frac{3}{2}x - 20$

Step-by-step explanation:

2 = ⅔[6] + b

4

$\displaystyle -2 = b \\ \\ y = \frac{2}{3}x - 2$

If you want it in Standard Form:

y = ⅔x - 2

- ⅔x - ⅔x

_________

−⅔x + y = −2 [We do not want fractions in our standard equation, so multiply by the denominator to get rid it.]

−3[−⅔x + y = −2]

$\displaystyle 2x - 3y = 6$

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−5 = 3⁄2[10] + b

15

$\displaystyle -20 = b \\ \\ y = \frac{3}{2}x - 20$

If you want it in Standard Form:

y = 3⁄2x - 20

- 3⁄2x - 3⁄2x

__________

−3⁄2x + y = −20 [We do not want fractions in our standard equation, so multiply by the denominator to get rid of it.]

−2[−3⁄2x + y = −20]

$\displaystyle 3x - 2y = 40$

* Parallel Lines have SIMILAR RATE OF CHANGES [SLOPES], so ⅔ and 3⁄2 remain the way they are.

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