Question

If P(x,y) is any point on the line joining the points A(a,0) and B(0,b) then show that $\frac{x}{a}+\frac{y}{b}=1$.

Answer 1

Let the equation of line be y = mx+c
A(a,0) and B(0,b) lie on this line
$\therefore O=ma+c\Rightarrow m=-\frac{c}{a}$
and $b=m\left(a\right)+c\Rightarrow c=b$
$\therefore y=(-\frac{c}{a})x+bory=(-\frac{b}{a})x\times b(\because c=b)$
Divide by b:
$\frac{y}{b}=-\frac{x}{b}+1$
or $\frac{x}{a}+\frac{y}{b}=1$ Proved
This is called 'intercept' form of equation of line and a, b are x and y intercepts