In the diagram, the line segment has slope $-\frac{3}{2}$.

The value of $b$ is
(A) 10
(B) 12
(C) 6
(D) 16
(E) 20

![](https://cdn.mathpix.com/cropped/2024_04_20_e85ef69091c57cb633f3g-110.jpg?height=437&width=439&top_left_y=1706&top_left_x=1293)
Solution 1

Since the slope is $-\frac{3}{2}$, then for every 2 units we move to the right along the line, we must move 3 units down.

![](https://cdn.mathpix.com/cropped/2024_04_20_688a3b42f69739f2e244g-201.jpg?height=441&width=441&top_left_y=1590&top_left_x=880)

To get from $(0, b)$ to $(8,0)$, we move 8 units right, or 2 units right four times. Therefore, we must move 3 units down four times, or 12 units down in total. Therefore, $b=12$.

Solution 2

Since the slope of the line is $-\frac{3}{2}$, then $\frac{b-0}{0-8}=-\frac{3}{2}$ or $-\frac{b}{8}=-\frac{3}{2}$ or $b=8 \times \frac{3}{2}=12$.

ANSWER: (B)