1. **State the problem:** Find the equation of the line passing through the points (0, 2) and (2, 0). 2. **Formula used:** The slope-intercept form of a line is given by $$y = mx + b$$ where $m$ is the slope and $b$ is the y-intercept. 3. **Calculate the slope $m$:** $$m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{0 - 2}{2 - 0} = \frac{-2}{2} = -1$$ 4. **Find the y-intercept $b$:** Since the line passes through (0, 2), the y-intercept is $b = 2$. 5. **Write the equation:** Substitute $m = -1$ and $b = 2$ into the slope-intercept form: $$y = -1 \cdot x + 2$$ 6. **Interpretation:** The line has a negative slope of $-1$, crosses the y-axis at 2, and crosses the x-axis where $y=0$. 7. **Find the x-intercept:** Set $y=0$: $$0 = -1 \cdot x + 2$$ $$\Rightarrow x = 2$$ 8. **Summary:** - Degree: 1 (linear) - Shape: Straight line - Leading Coefficient: -1 - Number of x-intercepts: 1 - x-intercept: 2 - y-intercept: 2 - End behavior: As $x \to \infty$, $y \to -\infty$; as $x \to -\infty$, $y \to \infty$ - Domain: All real numbers - Range: All real numbers - Number of Turning Points: 0 **Final equation:** $$y = -x + 2$$