The $y$-intercepts of three parallel lines are 2,3 and 4 . The sum of the $x$-intercepts of the three lines is 36 . What is the slope of these parallel lines?
(A) $-\frac{1}{3}$
(B) $-\frac{2}{9}$
(C) $-\frac{1}{6}$
(D) -4
(E) $-\frac{1}{4}$
Suppose the slope of the three parallel lines is $m$.

The equation of a line with slope $m$ and $y$-intercept 2 is $y=m x+2$.

To find the $x$-intercept in terms of $m$, we set $y=0$ and solve for $x$.

Doing this, we obtain $m x+2=0$ or $x=-\frac{2}{m}$.

Similarly, the line with slope $m$ and $y$-intercept 3 has $x$-intercept $-\frac{3}{m}$.

Also, the line with slope $m$ and $y$-intercept 4 has $x$-intercept $-\frac{4}{m}$.

Since the sum of the $x$-intercepts of these lines is 36 , then $\left(-\frac{2}{m}\right)+\left(-\frac{3}{m}\right)+\left(-\frac{4}{m}\right)=36$. Multiplying both sides by $m$, we obtain $-2-3-4=36 m$ and so $36 m=-9$ or $m=-\frac{1}{4}$.

ANSWER: (E)