What is the equation of the straight line cutting-off an intercept 2 from the negative direction of Y-axis and inclined at 30$$^\circ$$ with the positive direction of X-axis?

What is the equation of the line passing through the point of intersection of the lines $$x + 2y - 3 = 0$$ and $$2x - y + 5 = 0$$ and parallel to the line $$y - x + 10 = 0$$ ?

Consider the following statements

I. The length p of the perpendicular from the origin to the line ax + by = c satisfies the relation $${p^2} = {{{c^2}} \over {{a^2} + {b^2}}}$$.

II. The length p of the perpendicular from the origin to the line $${x \over a} + {y \over b} = 1$$ satisfied the relation $${1 \over {{p^2}}} = {1 \over {{a^2}}} + {1 \over {{b^2}}}$$.

III. The length p of the perpendicular from the origin to the line y = mx + c satisfies the relation $${1 \over {{p^2}}} = {{1 + {m^2} + {c^2}} \over {{c^2}}}$$.

Which of the above is/are correct?

What is the equation of the straight line passing through the point (2, 3) and making an intercept on the positive Y-axis equal to twice its intercept on the positive X-axis?