Question

Find the equation to the straight line which passes through the point (-4, 3) and is such that the portion of it between the axes is divided by the point in the ratio 5 : 3.

Answer 1

$\text{Let equation of line be}\frac{x}{a}+\frac{y}{b}=1\text{The line}\frac{x}{a}+\frac{y}{b}=1\text{intersects the axes at (a, 0) and (0, b)}\text{It is given (-4, 3) divides the line joining A (a, 0) and B (0, b) in ratio 5 : 3}\frac{5\times 0+3\times a}{5+3},\frac{5\times b+3\times 0}{5+3}=(-4,3)\therefore (\frac{3a}{8},.\frac{5b}{8})=(-4,3)\Rightarrow \frac{3a}{8}=-4\Rightarrow a=\frac{-32}{3}And\frac{5b}{8}=3\Rightarrow b=\frac{24}{5}\therefore \text{The equation of line is}\frac{3x}{-32}+\frac{5y}{24}=1or9x-20y+96=0$