Question

Reduce the equation $5x+7y-8=0$ to intercept form. Hence find the length of the segment intercepted between the axes.

Answer 1

The given equation is $5x+7y-8=0$

$\Rightarrow 5x+7y=8$

Dividing both sides by $8$, we get

$\Rightarrow \frac{5x}{8}+\frac{7y}{8}=1$

$\Rightarrow \frac{x}{\frac{8}{5}}+\frac{y}{\frac{8}{7}}=1$ which is the required intercept form.

Here $x-$intercept$=a=\frac{8}{5}$ and $y-$intercept$=b=\frac{8}{7}$

$\therefore$The length of the segment intercepted between the axes$=\sqrt{a^2+b^2}$

$=\sqrt{{\left(\frac{8}{5}\right)}^2+{\left(\frac{8}{7}\right)}^2}$

$=8\sqrt{\frac{1}{25}+\frac{1}{49}}$

$=8\sqrt{\frac{49+25}{25\times 49}}$

$=8\frac{\sqrt{74}}{5\times 7}$

$=\frac{8\sqrt{74}}{35}$ units