Question

The differential equation of all straight lines passing through the point $( 1 , - 1 )$is

• A. $y = ( x + 1 ) \frac { d y } { d x } + 1$
• B. $y = ( x + 1 ) \frac { d y } { d x } - 1$
• C. $y = ( x - 1 ) \frac { d y } { d x } + 1$
• D. $y = ( x - 1 ) \frac { d y } { d x } - 1$

Answer 1

Answer: (D)

$y = ( x - 1 ) \frac { d y } { d x } - 1$

Answer 2

Since the equation of line passing through (1,–1) is $y + 1 = m ( x - 1 )$

⇒ $y + 1 = \frac { d y } { d x } ( x - 1 )$ ⇒ $y = ( x - 1 ) \frac { d y } { d x } - 1$ .