Question

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

Answer 1

Given that P(x, y) be any point on the straight line AB cuts off intercepts a and b on x – axis at A (a, 0)and y – axis at B(0, b).
$\therefore$ Slope of the straight line $AB=-\frac{b}{a}$
Then the equation of straight line by the slope – intercept form
$\Rightarrow y=(-\frac{b}{a})x+b$
$\Rightarrow \frac{y}{b}=(-\frac{1}{a})x+1$
$\Rightarrow \frac{x}{a}+\frac{y}{b}=1$