4. \( y \geq \frac{1}{4} x-5 \)

Did you know that inequalities like this one can help us visualize relationships on a graph? Here, the line \( y = \frac{1}{4} x - 5 \) is the boundary, and since it’s a “greater than or equal to” inequality, we shade the area above the line. It's a fantastic way to represent constraints in real life, like budgeting or resource allocation! When working with inequalities, watch out for common slip-ups! A frequent mistake is forgetting to reverse the inequality sign when multiplying or dividing by a negative number. Always double-check your operations! It's also essential to label boundary lines correctly; solid lines mark “equal to” cases, while dashed lines indicate exclusivity—tiny details that can transform your graph!