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garik1379 [7]
3 years ago
9

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

Mathematics
1 answer:
vova2212 [387]3 years ago
3 0

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 <em>Standard Form</em>:

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

_______________________________________________

−5 = 3⁄2[10] + b

15

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

If you want it in <em>Standard</em><em> </em><em>Form</em>:

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 <em>RATE OF CHANGES</em> [<em>SLOPES</em>], so ⅔ and 3⁄2 remain the way they are.

I am joyous to assist you anytime.

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