1. The problem describes a triangular region bounded by three lines: $x=1$, $y=2$, and $x+y=10$. 2. To understand the shape and find the vertices of the triangle, we find the intersection points of these lines. 3. Intersection of $x=1$ and $y=2$ is the point $(1,2)$. 4. Intersection of $x=1$ and $x+y=10$: substitute $x=1$ into $x+y=10$ gives $1 + y = 10 \Rightarrow y = 9$, so the point is $(1,9)$. 5. Intersection of $y=2$ and $x+y=10$: substitute $y=2$ into $x+y=10$ gives $x + 2 = 10 \Rightarrow x = 8$, so the point is $(8,2)$. 6. The vertices of the triangle are therefore $(1,2)$, $(1,9)$, and $(8,2)$. 7. The triangle is bounded by the vertical line $x=1$, the horizontal line $y=2$, and the slanted line $x+y=10$ connecting $(1,9)$ and $(8,2)$. 8. The function representing the slanted line is $y = 10 - x$. 9. This fully describes the triangular region formed by these three lines.