Question

The equation of the line making ${53}^{\circ }$ with positive $x-axis$ and passing through $(2,4)$ is
[Hint:- $\tan {53}^{\circ }=\frac{4}{3}$]

• A. $3y-4x-4=0$
• B. $3y-2x+20=0$
• C. $y-2x+20=0$
• D. $3y-2x+10=0$

Answer 1

The correct option is A $3y-4x-4=0$

From the question, slope of the line is $m=\tan {53}^{\circ }=\frac{4}{3}$
Equation of the line is given as $y-y_1=m(x-x_1)$
$\Rightarrow y-\left(4\right)=\frac{4}{3}(x-2)$
$\Rightarrow 3(y-4)=4(x-2)$
$\Rightarrow 3y-4x-4=0$