To solve the second inequality graphically, we'll follow these steps:
1. Identify the inequality:
The second inequality is [tex]\( y \geq -6 \)[/tex].
2. Determine the type of line:
Since the inequality is [tex]\( y \geq -6 \)[/tex] (greater than or equal to), the boundary line will be solid.
3. Find two points on the boundary line:
We need to identify two points on the boundary line where [tex]\( y = -6 \)[/tex]. Two such points are:
- Point 1: [tex]\((0, -6)\)[/tex]
- Point 2: [tex]\((1, -6)\)[/tex]
4. Draw the boundary line:
- Draw a solid horizontal line passing through the points [tex]\((0, -6)\)[/tex] and [tex]\((1, -6)\)[/tex]. This line represents [tex]\( y = -6 \)[/tex].
5. Shade the solution region:
- Since the inequality is [tex]\( y \geq -6 \)[/tex], you need to shade the region above the boundary line. This indicates all the points that have [tex]\( y \)[/tex] values greater than or equal to [tex]\(-6\)[/tex].
In summary:
- The two points on the boundary line [tex]\( y = -6 \)[/tex] are [tex]\( (0, -6) \)[/tex] and [tex]\( (1, -6) \)[/tex].
- The boundary line is solid.
- The region above this line, where [tex]\( y \geq -6 \)[/tex], represents the solution set for the second inequality.
