2004 AMC 12A Problem 5

Attempt Problem 5 of the 2004 AMC 12A below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2004 AMC 12A solutions, or check the answer key.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

The graph of a line

y = mx + b

is shown. Which of the following is true?

mb \lt -1

-1 \lt mb \lt 0

mb = 0

0 \lt mb \lt 1

mb \gt 1

Read the sign and size of the slope

m

and the

y

-intercept

b

separately

Both

m

and

b

have absolute value less than

1,

but opposite signs

The

y

-intercept of the line is between

0

and

1,

0 \lt b \lt 1.

The slope is negative and shallow, between

-1

and

0,

-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.

Problem 5 in other years