The line $L$ crosses the $x$-axis at $(-8,0)$. The area of the shaded region is 16 . What is the slope of the line $L$ ?
(A) $\frac{1}{2}$
(B) 4
(C) $-\frac{1}{2}$
(D) 2
(E) -2

![](https://cdn.mathpix.com/cropped/2024_04_20_6ed09463f225f8ba1f07g-135.jpg?height=407&width=567&top_left_y=122&top_left_x=1256)
The line $L$ crosses the $x$-axis at $(-8,0)$. The area of the shaded region is 16 . What is the slope of the line $L$ ?
(A) $\frac{1}{2}$
(D) 2
(B) 4
(C) $-\frac{1}{2}$
(E) -2

![](https://cdn.mathpix.com/cropped/2024_04_20_faa9db06d997f2a5b9b1g-220.jpg?height=450&width=613&top_left_y=279&top_left_x=1298)

## Solution

If the area of the shaded region is 16 and its base has a length of 8 , its height must then be 4 .

Thus we have the changes noted in the diagram.

Thus the slope is $\frac{4-0}{0-(-8)}=\frac{1}{2}$ or $\frac{1}{2}$ because the line slopes down from right to left and the line has a rise of 4 and a run of 8 .

![](https://cdn.mathpix.com/cropped/2024_04_20_faa9db06d997f2a5b9b1g-220.jpg?height=450&width=632&top_left_y=775&top_left_x=1294)

$$
\text { Area }=\frac{1}{2}|-8||4|=16
$$

ANSWER: (A)