Question

The equation of a straight line passing through the point $(1,2)$ and inclined at ${45}^{\circ }$ to the line $y=2x+1$ is

• A. $5x+y=7$
• B. $3x+y=5$
• C. $x+y=3$
• D. $x-y+1=0$

Answer 1

The correct option is B $3x+y=5$

Let $y=mx+c$ be the equation then,
we know that when angle between two line is $\theta$, then
$tan\theta =\frac{m_1-m_2}{1+m_1{m}_2}$

$\tan 45°=\frac{m-2}{1+m\cdot 2}$

$\Rightarrow m-2=2m+1$

$\Rightarrow m=-3$

$\therefore y=-3x+c$ passes through $(1,2)$

$\therefore c=2+3=5$

$\therefore y+3x=5$ is the equation.