Graphing linear equations vs. inequalities: Key differences explained

📚 Understanding Linear Equations

A linear equation represents a straight line on a graph. It shows a relationship where the change between two variables is constant. The standard form is $y = mx + b$, where 'm' is the slope and 'b' is the y-intercept. When you graph a linear equation, you get a solid line because every point on that line is a solution to the equation.

📈 Understanding Linear Inequalities

A linear inequality, on the other hand, represents a region of the coordinate plane. Instead of an equals sign (=), it uses inequality symbols such as < (less than), > (greater than), ≤ (less than or equal to), or ≥ (greater than or equal to). This means that the solutions are not just points on a line, but rather all the points in a certain area. The boundary line can be either solid or dashed, depending on whether the inequality includes the 'equal to' part (≤ or ≥).

📊 Linear Equations vs. Linear Inequalities: A Detailed Comparison

🔑 Key Takeaways

• ✍️ Linear equations use an equals sign and graph as a solid line.
• 🗺️ Linear inequalities use inequality symbols and graph as a region, with either a solid or dashed boundary line.
• 💡 Understanding the difference in symbols is crucial for correctly graphing and interpreting the solutions.
• ➕ Solid lines include the values on the line, while dashed lines do not.
• 📌 Shading indicates all the possible solutions to the inequality.