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Let the equation of required line in intercept form be \frac{x}{a}+\frac{y}{b}=1

Since the line apsses through point (3,4) :

Also area of triangle formed with axes must be 24 :
\frac{1}{2}ab=24\implies b=\frac{48}{a}

Plug this value in earlier equation  and get

Thus the equation of straight line is \frac{x}{6}+\frac{y}{8}=1