Geo2.12

Find the equation of the straight line passing through $(3,-4)\,$ and making intercepts in the ratio 2:3.

Let the intercepts be $2k,3k\,$

Then the equation of the line is

$\frac{x}{2k}+\frac{y}{3k}=1\,$

$3xk+2yk=6\,$

Since the line passes through (3,-4)

$9k-8k=6\,$

Hence the equation is

$\frac{x}{12}+\frac{y}{18}=1\,$

$3x+2y=36\,$