2004 AMC 12A Problems/Problem 5

Problem

The graph of the line $y=mx+b$ is shown. Which of the following is true?

$\mathrm {(A)} mb<-1 \qquad \mathrm {(B)} -1<mb<0 \qquad \mathrm {(C)} mb=0 \qquad \mathrm {(D)}$ $0<mb<1 \qquad \mathrm {(E)} mb>1$

Solution

It looks like it has a slope of $-\dfrac{1}{2}<m<0$ (looking at the intercepts) and is shifted $0<b<1$ up. Try $m=-\dfrac{1}{3}$ and $b=\dfrac{4}{5}$ .

$\dfrac{4}{5}\cdot \dfrac{-1}{3}=\dfrac{-4}{15} \Rightarrow \mathrm {(B)}$

2004 AMC 12A (Problems • Answer Key • Resources)
Preceded by Problem 4	Followed by Problem 6
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2004 AMC 12A Problems/Problem 5

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