1. **Problem Statement:** We have a graph with a solid line passing through the origin with slope 1, and the region above and to the left of this line is shaded. 2. **Equation of the solid line:** The line passes through points (0,0) and (2,2). The slope $m$ is calculated as: $$m=\frac{2-0}{2-0}=1$$ Using point-slope form with point (0,0): $$y=mx+b$$ Since it passes through the origin, $b=0$, so: $$y=x$$ 3. **Algebraic inequality of the graph:** The shaded region is above the line $y=x$. Since the line is solid, points on the line satisfy the inequality. Thus, the inequality is: $$y\geq x$$ 4. **Effect of dashed line on inequality:** If the line were dashed, points on the line would not be included in the solution set. Therefore, the inequality would change to: $$y>x$$ Final answers: - a) Equation of the solid line: $y=x$ - b) Inequality for the shaded region: $y\geq x$ - c) If the line is dashed, inequality changes to: $y>x$