Linear Plot 2B4589

1. **State the problem:** We need to plot points for the linear equation $$y = -\frac{1}{2}x - 9$$ and connect them with a line. 2. **Formula and rules:** The equation is in slope-intercept form $$y = mx + b$$ where $$m$$ is the slope and $$b$$ is the y-intercept. 3. **Identify slope and intercept:** Here, $$m = -\frac{1}{2}$$ and $$b = -9$$. 4. **Plot the y-intercept:** The point where the line crosses the y-axis is at $$(0, -9)$$. 5. **Use the slope to find another point:** Slope $$-\frac{1}{2}$$ means for every increase of 2 in $$x$$, $$y$$ decreases by 1. 6. **Calculate second point:** Starting at $$(0, -9)$$, increase $$x$$ by 2: $$x = 2$$. Calculate $$y$$: $$y = -\frac{1}{2} \times 2 - 9 = -1 - 9 = -10$$ So second point is $$(2, -10)$$. 7. **Calculate third point:** Increase $$x$$ by another 2: $$x = 4$$. Calculate $$y$$: $$y = -\frac{1}{2} \times 4 - 9 = -2 - 9 = -11$$ Third point is $$(4, -11)$$. 8. **Plot points:** Plot $$(0, -9)$$, $$(2, -10)$$, and $$(4, -11)$$ on the coordinate grid. 9. **Draw the line:** Connect these points with a straight line extending in both directions. 10. **Summary:** The line has slope $$-\frac{1}{2}$$ and y-intercept $$-9$$, and points plotted are $$(0, -9)$$, $$(2, -10)$$, and $$(4, -11)$$.