First slide

Equation of line in Straight lines

Question

The angle between the line $x + 2 y - 5 = 0$ and the positive $x -$ axis is $θ$ then the value of $\sin θ$ is

Moderate

A

$\frac{1}{\sqrt{5}}$
B

$\frac{2}{\sqrt{5}}$
C

$\frac{3}{\sqrt{5}}$
D

$\frac{4}{\sqrt{5}}$

Solution

$The angle θ made by line with x -axis in positive direction is called inclination of the line.$
$The slope of the line a x + b y + c = 0 is m = - \frac{a}{b} and θ = \tan^{- 1} (- \frac{a}{b})$
$The slope of the line x + 2 y - 5 = 0 is m = - \frac{a}{b} = - \frac{1}{2}$
$If θ is inclination then \tan θ = - \frac{1}{2}, θ lies in the second quadrant.$
$Use right triangle the value for \sin θ = \frac{1}{\sqrt{5}}$

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