Question

The equation of the line passing through $(4,-6)$and makes an angle $45°$with positive$x$ axis, is

• A. $x-y-10=0$
• B. $x-2y-16=0$
• C. $x-3y-22=0$
• D. None of these

Answer 1

The correct option is A

$x-y-10=0$

Explanation of correct answer:

Equation of the line:

Given: angle $\theta =45°$

We know that, $\mathrm{slope}=\tan \left(\theta \right)$

$\Rightarrow$ $\mathrm{slope}=\tan \left(45°\right)$

$\Rightarrow$ $\mathrm{slope}=1$

Since, Equation of the line is given by,

$\left(y-y_1\right)=m\left(x-x_1\right)$

Line passing through $(4,-6)$is,

$\left(y+6\right)=1\left(x-4\right)$

$\Rightarrow$ $y+6=x-4$

$\Rightarrow$$x-y-10=0$

Hence, Option $\left(\mathrm{A}\right)$ is the correct answer.