1. The problem asks to write an inequality representing the shaded region on the graph. 2. The graph shows a line passing through points $(-2,-1)$ and $(2,1)$. 3. First, find the slope $m$ of the line using the formula: $$m=\frac{y_2-y_1}{x_2-x_1}=\frac{1-(-1)}{2-(-2)}=\frac{2}{4}=\frac{1}{2}$$ 4. Use point-slope form to find the equation of the line. Using point $(-2,-1)$: $$y - (-1) = \frac{1}{2}(x - (-2))$$ $$y + 1 = \frac{1}{2}(x + 2)$$ $$y + 1 = \frac{1}{2}x + 1$$ $$y = \frac{1}{2}x + 1 - 1$$ $$y = \frac{1}{2}x$$ 5. The line equation is $y = \frac{1}{2}x$. 6. The shaded region is to the right side of the line, including the line itself. 7. To determine the inequality, test a point not on the line, for example $(0,0)$: $$0 \geq \frac{1}{2} \times 0$$ $$0 \geq 0$$ which is true. 8. Since the test point satisfies $y \geq \frac{1}{2}x$, the inequality representing the shaded region is: $$y \geq \frac{1}{2}x$$