Question: From $x + 2y = 2$, we can express $y$ in terms of $x$: $y = \frac{2 - x}{2}$. Since $x \geq 0$ and $y \geq 0$, the limits for $x$ are from $0$ to $2$. Elaborate
1. **State the problem:** We start with the linear equation $$x + 2y = 2$$ and want to express $y$ in terms of $x$.
2. **Isolate $y$:** To express $y$ in terms of $x$, subtract $x$ from both sides:
$$x + 2y = 2 \implies 2y = 2 - x$$
3. **Divide both sides by 2:**
$$y = \frac{2 - x}{2}$$
4. **Consider the domain restrictions:** Since $x \geq 0$ and $y \geq 0$, we find the valid range for $x$.
5. **Find $x$ limits from $y \geq 0$:**
$$y = \frac{2 - x}{2} \geq 0 \implies 2 - x \geq 0 \implies x \leq 2$$
6. **Combine with $x \geq 0$:**
The domain for $x$ is $$0 \leq x \leq 2$$.
7. **Summary:**
- The function is $$y = \frac{2 - x}{2}$$.
- The domain is $$x \in [0, 2]$$.
- Both $x$ and $y$ are non-negative in this interval.
This means the line segment from $(0,1)$ to $(2,0)$ in the coordinate plane satisfies the equation and the given constraints.