Find the equation of line which passes through point $(2, 3)$ and makes an angle of $45^{o}$ with $x -$ axis.

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Solution

Given $θ = 45^{o}$
then $θ = m = tan 45^{o} = 1$
$\Rightarrow m = 1$
equation of line passing through point $(2, 3)$
$y - y_{1} = m (x - x_{1})$
$\Rightarrow y - 3 = 1 (x - 2)$
$\Rightarrow y - 3 = x - 2$
$\Rightarrow x - y + 3 - 2 = 0$
$\Rightarrow x - y + 1 = 0$
Thus required equation of straight line of
$x - y + 1 = 0$

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Find the equation of line which passes through point (2,3) and makes an angle of 45o with x−axis.

Given θ=45othen θ=m=tan45o=1⇒m=1equation of line passing through point (2,3)y−y1=m(x−x1)⇒y−3=1(x−2)⇒y−3=x−2⇒x−y+3−2=0⇒x−y+1=0Thus required equation of straight line of x−y+1=0

Find the equation of line which passes through point $(2, 3)$ and makes an angle of $45^{o}$ with $x -$ axis.