The equation of the straight line passing through the point $(3, 2)$ and perpendicular to the line $y = x$ is

Find the number of integer values of $m$ such that the $x$-coordinate of the point of intersection of the lines $3x + 4y = 9$ and $y = mx + 1$ is an integer.

The equation of the line passing through the point $(-3, 2)$ and parallel to the $x$-axis is:

Write the equation of the lines for which $\tan \theta = \frac{1}{2}$,where $\theta$ is the inclination of the line and $y$-intercept is $-\frac{3}{2}$.

If $u = a_1x + b_1y + c_1 = 0$,$v = a_2x + b_2y + c_2 = 0$ and $\frac{a_1}{a_2} = \frac{b_1}{b_2} = \frac{c_1}{c_2}$,then the curve $u + kv = 0$ is

One diagonal of a square is along the line $8x - 15y = 0$ and one of its vertices is $(1, 2)$. Then the equations of the sides of the square passing through this vertex are: