Let the intercepts made by the line on the x-axis and y-axis be a and (14-a) respectively.
Then, its equation is `(x)/(a)+(y)/((14-a))=1" "["intercept form"]`
Since it passes through the point (3,4), we have
`(3)/(a)+(4)/((14-a))=1 Leftrightarrow 3(14-a)+4a=a(14-a)`
`Leftrightarrow a^(2)-13a+42=0 Leftrightarrow (a-6)(a-7)=0`
`Leftrightarrow a=6 or a=7`
`"Now," a=b Leftrightarrow 14-6=8`
`"And" a=7 Leftrightarrow 14-7=7`
So, the required equation is
`(x)/(6)+(y)/(8)=1 or (x)/(7)+(y)/(7)=1`
`i.e. 4x+3y-24=0 or x+y-7=0`
