[size=150][color=#3d85c6]The intercept form of the equation of a line is as follows: [/color][math]\frac{x}{a}+\frac{y}{b}=1[/math][color=#3d85c6] where [/color][math]a[/math][color=#3d85c6] is the x-intercept and [/color][math]b[/math][color=#3d85c6]is the y-intercept of the line. [/color][color=#0000ff][br][/color][/size]Examine the applet below by dragging the points A and B . Here P is any point on the line . Drag P also and observe how the equation is obtained.
Why do we get the sum [math]\frac{x}{a}+\frac{y}{b}[/math] always equal to 1 whatever [math]a,b,x,y[/math]may be?
Similarity of the [math]\triangle EBP[/math]and [math]\triangle OBA[/math] implies [math]\frac{EP}{OA}=\frac{EB}{OB}\Rightarrow\frac{OD}{OA}=\frac{OB-OE}{OB}[/math][br][math]\Rightarrow\frac{x}{a}=1-\frac{y}{b}\Rightarrow\frac{x}{a}+\frac{y}{b}=1[/math]