$A$ line passes through the point $(3, 4)$ and cuts off intercepts from the coordinate axes such that their sum is $14$. The equation of the line is

The point $P(a, b)$ lies on the straight line $3x + 2y = 13$ and the point $Q(b, a)$ lies on the straight line $4x - y = 5$. Then the equation of the line $PQ$ is

The parallelism condition for two straight lines,one of which is specified by the equation $ax + by + c = 0$ and the other being represented parametrically by $x = \alpha t + \beta$ and $y = \gamma t + \delta$,is given by:

Reduce the following equation into slope-intercept form and find its slope and the $y$-intercept: $y=0$.

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 $(3, 0)$.

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