If the three points $A(1, 6)$, $B(3, -4)$, and $C(x, y)$ are collinear, then the equation satisfied by $x$ and $y$ is:

The points $\left( 0, \frac{8}{3} \right)$,$(1, 3)$,and $(82, 30)$

Find the equation of the line perpendicular to $5x - 2y + 7 = 0$ and passing through the intersection of the lines $y = x + 7$ and $x + 2y + 1 = 0$.

If the lines $L_1 \equiv 2x + y + 3 = 0$,$L_2 \equiv kx + 2y - 3 = 0$,and $L_3 \equiv 3x - 2y + 1 = 0$ are concurrent,then the cosine of the acute angle between the lines $L_2 = 0$ and $2x - 5y + 7 = 0$ is

If three lines whose equations are $y=m_{1}x+c_{1}$,$y=m_{2}x+c_{2}$,and $y=m_{3}x+c_{3}$ are concurrent,then show that $m_{1}(c_{2}-c_{3})+m_{2}(c_{3}-c_{1})+m_{3}(c_{1}-c_{2})=0$.

If the lines $x + 2ay + a = 0$,$x + 3by + b = 0$,and $x + 4cy + c = 0$ are concurrent,then $a, b,$ and $c$ are in which of the following?