Boundaries are very important when we graph linear inequalities. They help us understand where the solutions are located.

The linear equation that comes from the inequality creates a boundary line. For example, in the inequality y < 2x + 3, the boundary line is y = 2x + 3.

Types of Boundary Lines:

1. Solid Line:

   • We use this for inequalities like y ≤ mx + b or y ≥ mx + b.
   • This means the points on the line are part of the solution.

2. Dashed Line:

   • We use this for inequalities like y < mx + b or y > mx + b.
   • This means the points on the line are not part of the solution.

Finding the Shaded Region:

To figure out which side of the boundary line to shade, we can test a point. A common point to test is (0,0).

For the inequality y < 2x + 3, if we plug in (0, 0), we get 0 < 3.

Since this is true, we shade the area below the line.

This way of showing the graph helps us see where the solutions are in systems of inequalities. It makes it easier to find answers that work for all the conditions given.