Find the equation of a straight line passing through the point (0,4) and parallel toa line whose line is 3y−5x=5

Mathematics

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Answer

y=53x+4y = \frac{5}{3}x + 4

Step-by-step solution

3 steps

Ili kupata mlinganyo wa mstari ulionyooka, tunahitaji mteremko (slope) na sehemu ya kukata y (y-intercept) au nukta moja na mteremko.

  1. Tafuta mteremko wa mstari uliotolewa.

    Mstari uliotolewa ni 3y−5x=53y - 5x = 5. Tunahitaji kuuweka katika mfumo wa y=mx+cy = mx + c, ambapo mm ni mteremko.

    3y−5x=53y - 5x = 5

    Ongeza 5x5x pande zote mbili:

    3y=5x+53y = 5x + 5

    Gawanya kwa 3 pande zote mbili:

    y=53x+53y = \frac{5}{3}x + \frac{5}{3}

    Mteremko wa mstari huu ni m=53m = \frac{5}{3}.

  2. Tambua mteremko wa mstari mpya.

    Kwa kuwa mstari mpya unalingana (parallel) na mstari uliotolewa, una mteremko sawa.
    Hivyo, mteremko wa mstari mpya ni m=53m = \frac{5}{3}.

  3. Tumia nukta (0,4)(0,4) na mteremko m=53m = \frac{5}{3} kupata mlinganyo wa mstari.

    Nukta (0,4)(0,4) inamaanisha kuwa wakati x=0x=0, y=4y=4. Hii ndiyo sehemu ya kukata y (y-intercept), kwa hivyo c=4c=4.
    Tumia mfumo wa mlinganyo wa mstari y=mx+cy = mx + c:

    y=53x+4y = \frac{5}{3}x + 4
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