Question

The equation of the straight line which passes through the point $(2,-3)$ and makes an angle of $\frac{\pi }{4}$ with the axis of $x$ is

• A. $x-y=1$
• B. $x-y=5$
• C. $xy=1$
• D. $x+y=5$

Answer 1

Answer: (B)

$x-y=5$

Let the point be $P=(p,q)=(2,-3)$ and let the line make an angle $\theta =\frac{\pi }{4}$ with the positive $x-$axis

$⟹\tan \theta =\tan \frac{\pi }{4}=1=m$(Slope)

Now, the equation of a line passing through $(p,q)$ and making an angle $\theta$ with positive direction of $x-$axis is,

$y-q=m(x-p)$

$⟹y+3=1(x-2)$

$⟹x-y=5$

Hence, option B is correct.