$$line\ k\ has\ the\ equation=>Ax+By=C$$
$$Slope\ \left(m\right)=\frac{change\ in\ y}{change\ in\ x}=\frac{\triangle y}{\triangle x}=\frac{y}{x}$$
$$y=mx\ $$
Adding the intercept (c), the line of equation is in the form y = mx + c
Statement 1=> A=2B
$$Ax+By=C\ \ \ \ \ where\ A=2B$$
$$So,\ we\ have\ 2Bx+By=C$$
$$2x+y=\frac{C}{B}$$
$$y=-2x+\frac{C}{B}----\left(i\right)$$
Equation (i) is in the form y = mx + c. Hence, m=-2.
Therefore, statement 1 is SUFFICIENT.

Statement 2=> C=4B
$$Ax+By=C\ \ \ \ \ where\ C=4B$$
$$So,\ we\ have\ Ax+By=4B$$
$$Divide\ all\ through\ by\ B$$
$$We\ have;\ \frac{Ax}{B}+y=4$$
$$y=-\frac{A}{B}x+4\ \ \ -----\left(ii\right)$$
Equation (ii) is in the form y = mx + c. Hence, m=-A/B but the value of A and B are unknown, hence, statement 2 is INSUFFICIENT.

Conclusively, only statement 1 alone is sufficient. Hence, option A is the correct answer.