This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Ili kupata mlinganyo wa mstari ulionyooka, tunahitaji mteremko (slope) na sehemu ya kukata y (y-intercept) au nukta moja na mteremko. Step 1: Tafuta mteremko wa mstari uliotolewa. Mstari uliotolewa ni 3y - 5x = 5. Tunahitaji kuuweka katika mfumo wa y = mx + c, ambapo m ni mteremko. 3y - 5x = 5 Ongeza 5x pande zote mbili: 3y = 5x + 5 Gawanya kwa 3 pande zote mbili: y = (5)/(3)x + (5)/(3) Mteremko wa mstari huu ni m = (5)/(3). Step 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 = (5)/(3). Step 3: Tumia nukta (0,4) na mteremko m = (5)/(3) kupata mlinganyo wa mstari. Nukta (0,4) inamaanisha kuwa wakati x=0, y=4. Hii ndiyo sehemu ya kukata y (y-intercept), kwa hivyo c=4. Tumia mfumo wa mlinganyo wa mstari y = mx + c: y = (5)/(3)x + 4 Mlinganyo wa mstari ni: y = (5)/(3)x + 4 Tuma swali linalofuata 📸