In the diagram, the line with equation $y=2 x-8$ crosses the $x$-axis at $A$ and the $y$-axis at $B$. The area of $\triangle A O B$ is
(A) 8
(D) 32
(B) 16
(C) 12
(E) 4

![](https://cdn.mathpix.com/cropped/2024_04_20_e85ef69091c57cb633f3g-129.jpg?height=467&width=431&top_left_y=829&top_left_x=1324)
Point $B$ is the $y$-intercept of $y=2 x-8$, and so has coordinates $(0,-8)$ from the form of the line. Point $A$ is the $x$-intercept of $y=2 x-8$, so we set $y=0$ and obtain

$$
\begin{aligned}
0 & =2 x-8 \\
2 x & =8 \\
x & =4
\end{aligned}
$$

and so $A$ has coordinates $(4,0)$. This tells us that

Area of $\triangle A O B=\frac{1}{2}(O A)(O B)=\frac{1}{2}(4)(8)=16$.

![](https://cdn.mathpix.com/cropped/2024_04_20_688a3b42f69739f2e244g-231.jpg?height=552&width=504&top_left_y=1643&top_left_x=1298)

ANSWER: (B)