Graph these two lines on the same set of axes: $y=2x$ and $y=−\frac{1}{2}x+6$.

1. Find the $x$- and $y$-intercepts for each equation.

   Answer (a):

   The $y$-intercepts are $(0,0)$ and $(0,6)$, and the $x$-intercepts are $(0,0)$ and $(12,0)$.

2. Shade the region bounded by the two lines and the $x$-axis.

   Answer (b):

   

3. What are the domain and range of the region? How did you find these values?

   Hint (c):

   Look at the graph or the $x$-intercepts to find the domain. Find the point of intersection to determine the range.

   Answer (c):

   The domain is $0\le x\le12$, and the range is $0\le y\le4.8$.

4. Find the area of this region. Round your answer to the nearest tenth.

   Hint (d):

   What are the base and height of the triangle?