1. **State the problem:** We need to graph the line given by the equation $$y + 6 = -\frac{1}{2}(x + 10)$$. 2. **Rewrite the equation in slope-intercept form:** The slope-intercept form is $$y = mx + b$$ where $m$ is the slope and $b$ is the y-intercept. 3. **Simplify the given equation:** $$y + 6 = -\frac{1}{2}x - 5$$ Subtract 6 from both sides: $$y = -\frac{1}{2}x - 5 - 6$$ $$y = -\frac{1}{2}x - 11$$ 4. **Interpret the slope and intercept:** - Slope $m = -\frac{1}{2}$ means the line falls 1 unit vertically for every 2 units it moves horizontally to the right. - Y-intercept $b = -11$ means the line crosses the y-axis at $(0, -11)$. 5. **Plot points:** - At $x=0$, $y = -11$ (y-intercept). - At $x=2$, $y = -\frac{1}{2}(2) - 11 = -1 - 11 = -12$. - At $x=-10$, $y = -\frac{1}{2}(-10) - 11 = 5 - 11 = -6$ (which matches the original equation). 6. **Draw the line through these points on the Cartesian plane with x-axis and y-axis from -10 to 10.** **Final answer:** The line equation in slope-intercept form is $$y = -\frac{1}{2}x - 11$$.