Find the equation of the straight line passing through the point $(3, 4)$ such that the sum of its intercepts on the axes is $14$.

$A$ 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 $x$-intercept of a line passing through the points $\left(-\frac{1}{2}, 1\right)$ and $B(1, 3)$ is

The Fahrenheit temperature $F$ and absolute temperature $K$ satisfy a linear equation. Given that $K=273$ when $F=32$ and that $K=373$ when $F=212$. Express $K$ in terms of $F$ and find the value of $F$,when $K =0$.

$A$ straight line passes through $P(1, 2)$ such that its intercept between the axes is bisected at $P$. Its equation is:

If the normal form of the equation of a straight line $4x + 3y + 2 = 0$ is $x \cos \alpha + y \sin \alpha = p$ and its intercept form is $\frac{x}{a} + \frac{y}{b} = 1$,then $\frac{p \sec \alpha}{ab} = $