Question

Find the slope of the line which makes an angle 45 degree with the line x-2y=3

Answer 1

Answer:

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Answer 2

The slope of the line which makes an angle 45 degree with the line x-2y=3 is 1.

Explanation:

We know that , it $\theta$ is angle between two lines , then

$\tan\theta=\dfrac{m_2-m_1}{1-m_1m_2}$, where $m_1\ \&\ m_2$ are the slopes of two lines.   (1)

Let m be the slope of the line which makes an angle 45 degree with the line x-2y=3.

i.e. $\theta =45^{\circ}$

x-2y=3 can be written as $y=\dfrac{x}{2}-\dfrac{3}{2}$

As compared  $y=\dfrac{x}{2}-\dfrac{3}{2}$ to $y=bx+c$, where b is slope.

Slope of line $y=\dfrac{x}{2}-\dfrac{3}{2}$ is $\dfrac{1}{2}$   .

Substitute all values in (1), we get

$\tan45^{\circ}=\dfrac{m-\dfrac{1}{2}}{1-m\cdot \dfrac{1}{2}}\\\\\Rightarrow\ 1 =\dfrac{m-\dfrac{1}{2}}{1+\dfrac{m}{2}}\ \ \ [\because\tan45^{\circ}=1]\\\\\Rightarrow\ 1+\dfrac{m}{2}=m-\dfrac{1}{2}\\\\\Rightarrow\ 1+\dfrac{1}{2}=m-\dfrac{m}{2}\\\\\Rightarrow\ \dfrac{3}{2}=\dfrac{m}{2}\\\\\Rightarrow\ m=3$

Hence, the slope of the line which makes an angle 45 degree with the line x-2y=3 is 1.

# Learn more :

Find the slope of the line which makes an angle of 45° with the positive direction of x-axis​

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