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
x + y = 7
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