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Deepak Bora
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Write down the equation of the line whose gradient is 3/2 and which passes through P where P divides the line segment joining A (– 2, 6) and B (3, – 4) in the ratio 2 : 3.

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This question is Based on Equation of a Straight Line Chapter of M.L Aggarwal book for ICSE BOARD for class 10.
Here Given that:
A Gradient which passes through a point and that point divided a line segment joining two points in a ratio
Find out the equation of the line.
This is the Question Number 26, Exercise 12.1 of M.L Aggarwal.

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  1. Given, P divides the line segment joining the points A (-2, 6) and B (3, -4) in the ratio 2: 3

    So, the co-ordinates of P will be

    x = (m1x2 + m2x1)/(m1 + m2)

    = (2×3 + 3×(-2))/ (2 + 3)

    = (6 – 6)/5

    = 0/5 = 0

    y = (m1y2 + m2y1)/(m1 + m2)

    = (2×(-4) + 3×(6))/ (2 + 3)

    = (-8 + 18)/5 = 10/5

    = 2

    Hence, the co-ordinates of P are (0, 2)

    Now, the slope (m) of the line passing through (0, 2) is 3/2

    Thus, the equation will be

    y – y1 = m (x – x1)

    y – 2 = 3/2 (x – 0)

    2y – 4 = 3x

    ⇒ 3x – 2y + 4 = 0

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