Question

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

Answer 1

It a point (x,y) lies on a line joining the formula $A(x_1,y_1)$

and $B(x_2,y_2)$ the equation of the line is given by

$\frac{y-y_1}{x-x_1}=\frac{y_2-y_1}{x_2-x_1}$

Point $P(x,y)$ lies on the line joining the point $A(a,0)$

and $B(0,b)$ So

$\frac{y-0}{x-a}=\frac{b-0}{0-a}\Rightarrow \frac{a}{x-a}=\frac{-b}{a}\Rightarrow ay=-b(x-a)$

$\Rightarrow ay=-bx+ab\Rightarrow ay+bx=ab$

divide both sector by ab

$\frac{ay}{ab}+\frac{bx}{ab}=\frac{ab}{ab}$

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