2013 AMC 12B Problems/Problem 8

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 $l_3$ ?

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

Solution

2013 AMC 12B (Problems • Answer Key • Resources)
Preceded by Problem 7	Followed by Problem 9
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25
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2013 AMC 12B Problems/Problem 8

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