Question

直线 $y = mx + b$ 的图像如下。下列哪一项正确？

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

$mb \lt -1$

$-1 \lt mb \lt 0$

$mb = 0$

$0 \lt mb \lt 1$

$mb \gt 1$

$y$ 截距在 $0$ 和 $1$ 之间，所以 $0 \lt b \lt 1$ 。

斜率为负且较平缓，在 $-1$ 和 $0$ 之间，所以 $-1 \lt m \lt 0$ 。

因此乘积 $mb$ 为负，且绝对值小于 $1$ 得到 $-1 \lt mb \lt 0$ 。

所以正确答案是 B。

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.