Question

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