State the conditions where these formulas are used.
1) Equation of line in double intercept form.
2) Equation of line in two point form.
3) Equation of line in slope point form.
4) Equation of line in slope intercept form.

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Solution

Dear student
$3) T h e e q u a t i o n o f a l i n e w h i c h p a s s e s t h r o u g h t h e p o i n t (x_{1}, y_{1}) a n d h a s t h e s l o p e m i s y - y_{1} = m (x - x_{1}) L e t Q (x_{1}, y_{1}) b e t h e p o i n t t h r o u g h w h i c h t h e l i n e p a s s e s a n d l e t P (x, y) b e a n y p o i n t o n t h e l i n e . T h e n, s l o p e o f t h e l i n e i s, \frac{y - y_{1}}{x - x_{1}} B u t, m i s t h e s l o p e o f t h e l i n e . T h e r e f o r e, m = \frac{y - y_{1}}{x - x_{1}} \Rightarrow y - y_{1} = m (x - x_{1}) H e n c e, y - y_{1} = m (x - x_{1}) i s t h e r e q u i r e d e q u a t i o n o f t h e l i n e .$
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