1. **State the problem:** We need to graph the inequality $$2x - 5y \leq -10$$ on the coordinate plane. 2. **Rewrite the inequality in slope-intercept form:** To graph, solve for $y$. $$2x - 5y \leq -10$$ Subtract $2x$ from both sides: $$-5y \leq -10 - 2x$$ Divide both sides by $-5$. Remember, dividing by a negative number reverses the inequality sign: $$y \geq \frac{-10 - 2x}{-5}$$ Simplify the fraction: $$y \geq \frac{\cancel{-10} + \cancel{2x}}{\cancel{-5}} = 2 + \frac{2}{5}x$$ So, $$y \geq 2 + \frac{2}{5}x$$ 3. **Interpret the inequality:** The graph is the region above or on the line $y = 2 + \frac{2}{5}x$. 4. **Graph the boundary line:** Plot the line $y = 2 + \frac{2}{5}x$. This line is solid because the inequality includes equality ($\leq$). 5. **Shade the region:** Since $y$ is greater than or equal to the line, shade the area above the line. This completes the graphing of the inequality.