Math, asked by sonujoshi5364, 1 month ago

Find out equation of line which is passing through (-2, 4) and x intercept is 3 more than y intercept.​

Answers

Answered by MysticSohamS
0

Answer:

hey here is your solution

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Step-by-step explanation:

so \: for \: a \: certain \: line \\ given \: points \: are \: ( - 2,4) \\ so \: let \\ (x,y) = ( - 2,4) \\  \\ now \: here \: let \: its \\ x - intercept \: be \: a \: and \: its \: y - intercept \: be \: b \\ so \: here \:  \\ a = b + 3 \:  \:  \:  \: \:  \:  \:  \:  \:  \:  (1)

so \: we \: know \: that \\ double \: intercept \: of \: line \: is \: given \: by \\  \frac{x}{a}  +  \frac{y}{b}  = 1 \\  \\  \frac{ - 2}{a}  +  \frac{4}{b}  = 1 \\  \\  \frac{ - 2}{b + 3}  +  \frac{4}{b}  = 1 \\  \\  \:  \:  \frac{ - 2b + 4(b + 3)}{b(b + 3)}  = 1 \\  \\  - 2b + 4b + 12 = b(b + 3)  \\ 2b + 12 = b {}^{2}  + 3b \\ b {}^{2}  + 3b - 2b - 12 = 0 \\  \\ b {}^{2}  + b - 12 = 0 \\ b {}^{2}  + 4b - 3b - 12 = 0 \\ b(b + 4) - 3(b + 4) = 0 \\ (b - 3)(b + 4) = 0 \\ ie \:  \: b - 3 = 0 \:  \: or \:  \: b + 4 = 0 \\ b = 3  \:  \: or \:  \: b =  - 4

but \: as \: here \\ a = b + 3 \\ which \: means \: that \:  \: a > b \\  \\ so \: hence \: b =  - 4 \:  \: is \: absurd \\ thus \: b = 3 \\  \\ on \: substituting \: value \: of \: b \: in \: (1) \: as \: 3 \\ we \: get \\  \: a = 6

so \: using \\  \frac{x}{a}  +  \frac{y}{b}  = 1 \\  \\  \frac{ x}{6}  +  \frac{y}{3}  = 1 \\  \\   \frac{3x + 6y}{(6 \times 3)}  = 1 \\   \\ 3x + 6y = (6 \times 3) \\ 3x + 6y = 18 \\ 3(x + 2y) = 18 \\ \: x + 2y = 6 \\  \\ ie \:  \: x + 2y - 6 = 0

hence \: equation  \: of  \: line \:  which \:  is  \: passing  \: through \:  (-2, 4)  \\ and \:  x  - intercept \:  is  \: 3  \: more \:  than \:  y -  intercept. \: is \\ x + 2y - 6 = 0

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