Match the given angles with the corresponding slopes.

0

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Not defined

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- \sqrt{3}

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- \sqrt{\frac{1}{3}}

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Solution

If $θ$ be the angle at which a straight line is inclined to the positive direction of x-axis, the slope of the line is defined by $m = t a n θ$ where $0^{\circ} \leq θ < 180^{\circ} θ \neq 90^{\circ}$
1. when $θ = 0^{\circ}$
Slope = $t a n θ = t a n 0^{\circ} = 0$

2. when $θ = 90^{\circ}$
at $θ$ = $90^{\circ}$ slope of the line is NOT defined

3. when $θ = 120^{\circ}$
Slope of line = $t a n 120^{\circ} = t a n (180^{\circ} - 60^{\circ}) = - t a n 60^{\circ} = - \sqrt{3}$

4. when $θ = 150^{\circ}$
Slope of line = $t a n 150^{\circ} = t a n (180^{\circ} - 30^{\circ}) = - t a n 30^{o} = - \frac{1}{\sqrt{3}}$

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Q. Match the given angles with the corresponding slopes.

\begin{matrix} P o s i t i v e x - d i r e c t i o n & S l o p e o f l i n e 1.) 0^{o} & p .) 0 2.) 90^{o} & q .) - \sqrt{3} 3.) 120^{o} & r .) - \frac{1}{\sqrt{3}} 4.) 150^{o} & s .) N o t d e f i n e d \end{matrix}

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