Question

A line passes through the point $(3,4)$ and cut off intercepts from the coordinates axes such that their sum is $14$. The equation of the line is

• A. $4x-3y=24$
• B. $4x+3y=24$
• C. $3x-4y=24$
• D. $3x+4y=24$

Answer 1

The correct option is B $4x+3y=24$

Let the intercept by the line on the axes are $a$ and $(14-a)$

Thus the equation,

$\frac{x}{a}+\frac{y}{14-a}=1$ and passes through $(3,4)$ ----- (1)

$\frac{3}{a}+\frac{4}{(14-a)}=1$

Therefore,

$a=6,b=8$

So the equation is

Put in (1)

$4x+3y=24$