If P(x , y) is any point on the line joining the points A (a , 0) and B(0 , b) , then show that

If P(x , y) is any point on the line joining the points A (a , 0) and

1.	If P(x , y) is any point on the line joining the points A (a , 0) and B(0 , b) , then show that
Answer» If a POINT (X,y) lies on a line JOINING the points A(x₁,y₁) and B(x₂,y₂), 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 points A(a,0) and B(0,b). So $\frac{y-0}{x-a} = \frac{b-0}{0-a} \\ \\ \Rightarrow \frac{y}{x-a}=- \frac{b}{a} \\ \\ \Rightarrow ay=-b(x-a)\\ \\ \Rightarrow ay=-bx+ab\\ \\ \Rightarrow ay+bx=ab\\ \\divide\ both\ sides\ by\ ab\\ \\ \Rightarrow \frac{ay}{ab}+ \frac{bx}{ab} = \frac{ab}{ab}\\ \\ \Rightarrow \frac{y}{b}+ \frac{x}{a} =1\ (proved)$