1. **Stating the problem:** We are given the linear equation $x + y = 8$ and asked to understand its graph and properties. 2. **Formula and rules:** This is a linear equation in two variables $x$ and $y$. The general form is $Ax + By = C$, where $A=1$, $B=1$, and $C=8$. 3. **Finding intercepts:** - To find the $x$-intercept, set $y=0$: $$x + 0 = 8 \implies x = 8$$ - To find the $y$-intercept, set $x=0$: $$0 + y = 8 \implies y = 8$$ 4. **Graph description:** The line passes through points $(8,0)$ and $(0,8)$. 5. **Shaded region:** The top-left region of the grid is shaded, which corresponds to the inequality $x + y \leq 8$ or $x + y < 8$ depending on the context. 6. **Summary:** The line $x + y = 8$ divides the plane into two halves. Points on the line satisfy the equation exactly, and the shaded region represents all points where the sum of $x$ and $y$ is less than or equal to 8. Final answer: The line $x + y = 8$ has intercepts at $(8,0)$ and $(0,8)$ and divides the plane into two regions, with the top-left region shaded representing $x + y \leq 8$.