Interceptor !

Since Point A bisects the segment connecting the intercepts, $A(3,4)$ is the $midpoint$ of the intercepts $(a,0)$ and $(0,b)$ .

Midpoint Formula:

$(\frac{a+0}{2}, \frac{0+b}{2}) = (3,4)$

So we can get $a=6$ , $b=8$ .

Two-Point Formula:

$y-0=(\frac{8-0}{0-6})(x-6)$

Thus arriving at the equation of the line: $4x+3y=24$

I know this is a very easy problem.....but please refrain from plugging the values directly into the given equations and then getting the answer right!!!!

X intercept of the line= 3*2=6

Y intercept of the line= 4*2=8

Equation of the line= (x/6) +(y/8)=1 = 4x+3y=24

I know that this is not the best way, but here goes...

We are given that point $A(3,4)$ lies on the required line. Substituting the point in the given equations, we get the line equation to be $\displaystyle l : 4x + 3y = 24$