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

Let $u = \hat{i} - 2\hat{j}$ and $v = -3\hat{i} + 5\hat{j}$. Consider three points $P, Q,$ and $R$ having position vectors $-\frac{1}{7}\hat{i}$,$-\frac{1}{4}\hat{j}$,and $-2\hat{i} + 3\hat{j}$ respectively. Among these,the points on the line segment passing through $u$ and $v$ are

Find the equation of the line perpendicular to the line $x-7y+5=0$ and having $x$-intercept $3$.

The polar equation of the line perpendicular to the line $\sin \theta - \cos \theta = \frac{1}{r}$ and passing through the point $\left(2, \frac{\pi}{6}\right)$ is

The slope of a line that makes intercepts of equal length on the axes is:

Find the equation of the line passing through the point $(-2, 3)$ with a slope of $-4$.