Find the equation of a line that makes an intercept of $-3$ on the $y$-axis and makes an angle of ${\tan ^{ - 1}}\frac{3}{5}$ with the $x$-axis.

Find the equations of the sides $QR$ and $RP$ of a triangle $PQR$ where $P = (2, 1)$,and the sides $QR$ and $RP$ have slopes $m_1 = \frac{2}{\sqrt{3}}$ and $m_2 = -\frac{2}{\sqrt{3}}$ respectively,passing through the origin $(0, 0)$ for $QR$ and intersecting at $P(2, 1)$ for $RP$.

Find the equation of the line that bisects the line segment joining the points $(5, 3)$ and $(4, 4)$ and makes an angle of $45^{\circ}$ with the positive direction of the $x$-axis.

If $p = a_1 x + b_1 y + k_1 = 0$,$q = a_2 x + b_2 y + k_2 = 0$ and $\frac{a_1}{a_2} = \frac{b_1}{b_2} = \frac{k_1}{k_2}$,then the curve $p + c q = 0$ is

Find the slope of the line making an inclination of $60^{\circ}$ with the positive direction of the $x$-axis.

Match the items given in List-$I$ to the items given in List-$II$.

List-$I$	List-$II$
$A$. Line passing through $(-4, 3)$ and having intercepts in the ratio $5:3$	$1$. $2x - 5y + 4 = 0$
$B$. Line passing through $P(2, -5)$ such that $P$ bisects the part intercepted between the axes	$2$. $3x + 5y = 3$
$C$. Line parallel to $2x - 3y + 5 = 0$ with $x$-intercept $\frac{2}{5}$ is	$3$. $10x - 15y + 4 = 0$
$D$. Line perpendicular to $5x + 2y + 7 = 0$ with $y$-intercept $\frac{4}{5}$ is	$4$. $10x - 15y = 4$
	$5$. $5x - 2y - 20 = 0$