Question

# Find the equation of a straight line which passes through the point (3, 4) and sum of its intercepts on the x and y axis is 14.

A

x + y = 7

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B

4x + 3y = 24

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C

x + y = 14

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D

3x + 4y = 24

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Solution

## The correct option is B 4x + 3y = 24 Let intercept on x and y-axis be a & b. Equation of the time be xa+yb=1 This equation passes through (3,4) Therefore 3a+4b=1-------------(1) Given, a + b =14 b = 14 - a -----------------(2) Substituting the value of b in equation (1) 3a+4(14−a)=1 42−3a+4aa(14−a)=1 42+a=14a−a2 a2−13a+42=0 (a - 7) (a - 6) = 0 a = 7,6 For a = 7, b = 14 - 7 = 7 For a = 6, b = 14 - 6 = 8 Substituting the value of a and b in equation (1) We get the equations of lines x7+y7=1 and x6+y8=1 x + y = 7 and 4x + 3y = 24

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