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Mathematics

Points A(x, y), B(3, -2) and C(4, -5) are collinear. The value of y in terms of x is ∶

  1. 3x - 11

  2. 11 - 3x

  3. 3x - 7

  4. 7 - 3x

Straight Line Eq

ICSE 2024

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Answer

Since, points A, B and C are collinear.

∴ Slope of AB = Slope of BC.

2y3x=5(2)432y3x=5+212y3x=32y=3(3x)2y=9+3xy=2+93xy=73x.\Rightarrow \dfrac{-2 - y}{3 - x} = \dfrac{-5 - (-2)}{4 - 3} \\[1em] \Rightarrow \dfrac{-2 - y}{3 - x} = \dfrac{-5 + 2}{1} \\[1em] \Rightarrow \dfrac{-2 - y}{3 - x} = -3 \\[1em] \Rightarrow -2 - y = -3(3 - x) \\[1em] \Rightarrow -2 - y = -9 + 3x \\[1em] \Rightarrow y = -2 + 9 - 3x \\[1em] \Rightarrow y = 7 - 3x.

Hence, Option 4 is the correct option.

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