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2013 AMC 12B Problems/Problem 8

Revision as of 14:54, 22 February 2013 by Zverevab (talk | contribs) (Created page with "==Problem== Line <math>l_1</math> has equation <math>3x - 2y = 1</math> and goes through <math>A = (-1, -2)</math>. Line <math>l_2</math> has equation <math>y = 1</math> and meet...")
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Problem

Line $l_1$ has equation $3x - 2y = 1$ and goes through $A = (-1, -2)$. Line $l_2$ has equation $y = 1$ and meets line $l_1$ at point $B$. Line $l_3$ has positive slope, goes through point $A$, and meets $l_2$ at point $C$. The area of $\triangle ABC$ is 3. What is the slope of $l_3$?

$\textbf{(A)}\ \frac{2}{3} \qquad \textbf{(B)}\ \frac{3}{4} \qquad \textbf{(C)}\ 1 \qquad \textbf{(D)}\ \frac{4}{3} \qquad \textbf{(E)}\ \frac{3}{2}$

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