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Deepak Bora
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Find the equation of a straight line perpendicular to the line 3x – 4y + 12 = 0 and having same y-intercept as 2x – y + 5 = 0.

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This is the Important question of class 10 Based on Equation of a Straight Line Chapter of M.L Aggarwal book for ICSE BOARD.
Here you have to find the equation of a straight line perpendicular to a line and having same y-intercept as given in the question.
This is the Question Number 13, Exercise 12.2 of M.L Aggarwal.

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  1. Given line: 3x – 4y + 12 = 0

    The slope of the line is given by

    3x – 4y + 12 = 0 ⇒ 4y = 3x + 12

    y = (3/4) x + 3

    Thus, slope (m1) = ¾

    Now, let the slope of the line perpendicular to the given line be taken as m2

    So,

    m1 x m2 = -1

    (3/4) x m2 = -1

    m2 = -4/3

    And given, the y-intercept of the line is same as 2x – y + 5 = 0

    ⇒ y = 2x + 5

    So, the y-intercept is 5 = c.

    Hence, the equation of line is given by

    y = m2x + c

    y = (-4/3) x + 5

    3y = -4x + 15

    4x + 3y = 15

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