Question

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

(10, -5) y= 3/2x-7

(6,2) y= 2/3x+19​

Answer 1

`\displaystyle 2x - 3y = 6\:OR\:y = (2)/(3)x - 2 \\ \\ 3x - 2y = 40\:OR\:y = (3)/(2)x - 20`

Explanation:

2 = ⅔[6] + b

4

`\displaystyle -2 = b \\ \\ y = (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 = (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.

I am joyous to assist you anytime.