2004 AMC 12A Problem 5

The $y$-intercept of the line is between $0$ and $1,$ so $0 \lt b \lt 1.$ The slope is negative and shallow, between $-1$ and $0,$ so $-1 \lt m \lt 0.$ The product $mb$ is therefore negative with absolute value less than $1,$ giving $-1 \lt mb \lt 0.$ Thus, the correct answer is B.