Reduce the equation 5x – 12y = 60 to intercepts form.
Question:

Reduce the equation 5x – 12y = 60 to intercepts form. Hence, find the length of the portion of the line intercepted between the axes

Solution:

Given equation is $5 x-12 y=60$

We can rewrite it as

$\frac{5}{60} x-\frac{12}{60} y=1$

$\Rightarrow \frac{x}{12}-\frac{y}{5}=1$

$\Rightarrow \frac{x}{12}+\frac{y}{-5}=1$

This equation is in the slope intercept form i.e. in the form

$\frac{x}{a}+\frac{y}{b}=1$

Where, $x$-intercept $=12$ and $y$-intercept $=-5$

Two points are: $(12,0)$ on the $x$-axis and $(0,-5)$ on $y$-axis

We know the distance between two points $\left(\mathrm{x}_{1}, \mathrm{y}_{1}\right),\left(\mathrm{x}_{2}, \mathrm{y}_{2}\right)$ is

$=\sqrt{\left(x_{1}-x_{2}\right)^{2}+\left(y_{1}-y_{2}\right)^{2}}$

Length of the line

$=\sqrt{(12-0)^{2}+(0+5)^{2}}$

$=\sqrt{144+25}$

$=\sqrt{169}$

$=13$