Question

Find the equation of the line having an inclination ${60}^{\circ }$ with the positive direction of $X$axis and cut off an intercept of $\frac{5}{2}$ on the positive side of $Y$ axis.

Answer 1

The intercept is cut off on the positive side of $Y$ axis

$\therefore c=\frac{5}{2}$

Slope$=m=\tan \theta$

$m=\tan {60}^{\circ }=\sqrt{3}$

Equation of the line is $y=mx+c$

$y=\sqrt{3}\times x+\frac{5}{2}$

$\therefore$ Equation of the line is $2\sqrt{3}x-2y+5=0$