If the line passing through the points $(4, 3)$ and $(2, \lambda)$ is perpendicular to the line $y = 2x + 3$,then find the value of $\lambda$.

If the coordinates of the points $A$ and $B$ are $(1, 0)$ and $(2, \sqrt{3})$,then the angle made by the line $AB$ with the $x$-axis is .....$^o$.

Find the equation of the line which passes through $(0, 0)$ with slope $m$.

The equation of the line which cuts off an intercept $3$ units on $OX$ and an intercept $-2$ units on $OY$ is:

The equations of the sides $AB$,$AC$,and $BC$ of a $\triangle ABC$ are respectively $x-3y=0$,$3x-y=0$,and $x+y+4=0$. If $P$ and $Q$ are points on the line $3x-y+k=0$ passing through $B$ such that $PB:BQ=1:1$,then $k=$

The length $L$ (in centimetre) of a copper rod is a linear function of its Celsius temperature $C$. In an experiment,if $L = 124.942$ when $C = 20$ and $L = 125.134$ when $C = 110,$ express $L$ in terms of $C$.