Find the slope of the line passing through the points $(3, -2)$ and $(3, 4)$.

An equation of a line whose segment between the coordinate axes is divided by the point $\left(\frac{1}{2}, \frac{1}{3}\right)$ in the ratio $2: 3$ is

Find the value of $k$ for which the line $(k-3) x - (4-k^2) y + k^2 - 7k + 6 = 0$ passes through the origin.

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

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

If the slope of the line $ax + (3 - a)y + 7 = 0$ is $7$,then the value of the integral part of '$a$' is