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Question

Find the equation of 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 options are
A

x + y = 7


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(14a)=1

423a+4aa(14a)=1

42+a=14aa2

a213a+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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