Find the value of $k$,if the line joining the points $(2, k)$ and $(3, 7)$ is parallel to the line joining points $(-2, 1)$ and $(3, 0)$.

The lines $2x + 3y = 6$ and $2x + 3y = 8$ cut the $X$-axis at $A$ and $B$,respectively. $A$ line $L$ drawn through the point $(2, 2)$ meets the $X$-axis at $C$ in such a way that the abscissae of $A, B,$ and $C$ are in arithmetic progression. Then,the equation of the line $L$ is

Reduce the following equation into intercept form and find its intercepts on the axes: $3x + 2y - 12 = 0$.

$a$ and $b$ are the intercepts made by a line on the coordinate axes. If $3a = b$ and the line passes through $(1, 3)$,then the equation of the line is

$A$ line cuts off equal intercepts on the coordinate axes. The angle made by this line with the positive direction of the $X$-axis is: (in $^{\circ}$)

The line joining two points $A(2, 0)$ and $B(3, 1)$ is rotated about $A$ in the anticlockwise direction through an angle of $15^{\circ}$. The equation of the line in the new position is: