Question

Reduce the equation $3x-2y+4=0$ to intercepts form and find the length of the segment interceped between the axes.

Answer 1

$3x-2y+4=0$

$2y=3x+4$

$y=\frac{3}{2}+2$

$y=mx+c$

$\Rightarrow m=\frac{3}{2},c=2$

$3x-2y=-4$

$-\frac{3}{4}x+\frac{1}{2}y=1$

$\therefore \frac{x}{-\frac{4}{3}}+\frac{y}{2}=1$

Length of segment intercepted,

$=\sqrt{{(-\frac{4}{3})}^2+2^2}$

$=\sqrt{\frac{16}{9}+4}$

$=\frac{2\sqrt{13}}{3}$units