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JEE Main & Advanced Mathematics Straight Line Question Bank Slope of line, Equation of line in different forms

  • question_answer
    A line passes through the point (3, 4) and cuts off intercepts from the coordinates axes such that their sum is 14. The equation of the line is   

    A)            \[4x-3y=24\]                           

    B)            \[4x+3y=24\]

    C)            \[3x-4y=24\]                           

    D)            \[3x+4y=24\]

    Correct Answer: B

    Solution :

               Given \[a+b=14\Rightarrow a=14-b\]                    Hence the equation of straight line is \[\frac{x}{14-b}+\frac{y}{b}=1\].                    Also, it passes through \[(3,4)\]                    \[\therefore \] \[\frac{3}{14-b}+\frac{4}{b}=1\Rightarrow b=8\]or 7                    Therefore equations are \[4x+3y=24\]and\[x+y=7\].                    Trick: This question can be checked with the options as the line \[4x+3y=24\]passes through (3, 4) and also cuts the intercepts from the axes whose sum is 14.


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