Consider the equation $y - y_1 = m(x - x_1)$. If $m$ and $x_1$ are fixed and different lines are drawn for different values of $y_1$,then:

Write the equation of the lines for which $\tan \theta = \frac{1}{2}$,where $\theta$ is the inclination of the line and $x$-intercept is $4$.

If the line $px - qy = r$ intersects the coordinate axes at $(a, 0)$ and $(0, b)$,then the value of $(a + b)$ is equal to

If the $x-$intercept of some line $L$ is double that of the line $3x + 4y = 12$ and the $y-$intercept of $L$ is half that of the same line,then the slope of $L$ is

$A$ straight line parallel to the line $y=\sqrt{3}x$ passes through $Q(2,3)$ and cuts the line $2x+4y-27=0$ at $P$. Then the length of the line segment $PQ$ is

$A$ man is walking on a straight line. The arithmetic mean of the reciprocals of the intercepts of this line on the coordinate axes is $\frac{1}{4}$. Three stones $A, B$ and $C$ are placed at the points $(1,1), (2,2)$ and $(4,4)$ respectively. Which of these stones is/are on the path of the man?