First slide

Equation of line in Straight lines

Question

$Equation of the line passing through the point (5, 4) and making an angle 45^{\circ} with$ $negative direction of x - axis is$

Moderate

A

$x - y - 9 = 0$
B

$2 x - y - 9 = 0$
C

$x + y - 15 = 0$
D

$x + y - 9 = 0$

Solution

$Equation of line passing through the point (x_{1}, y_{1}) and having slope m is y - y_{1} = m (x - x_{1})$
$Here m = \tan θ, where θ is angle made by the line with x - axis in the positive direction.$
$Since the line making an angle 45^{\circ} with negative direction of x - axis, the angle made by the$
$line with positive direction of x - axis is 180^{\circ} - 45^{\circ} = 135^{\circ}$
$Hence the slope of the line is m = \tan (135^{\circ}) = - 1$
$The equation of the line passing through the point (5, 4) and having slope - 1 is$
$\begin{aligned} y - 4 = - (x - 5) \\ y - 4 = - x + 5 \\ x + y - 9 = 0 \end{aligned}$
$Therefore, the equation of the line is x + y - 9 = 0$

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