To determine the correct description of the graph for the inequality [tex]\( y \leq -2x + 3 \)[/tex], let's analyze each component of the inequality step-by-step.
1. Identify the boundary line:
The given inequality is [tex]\( y \leq -2x + 3 \)[/tex]. The boundary line here is [tex]\( y = -2x + 3 \)[/tex].
2. Type of boundary line:
- Since the inequality is [tex]\( \leq \)[/tex] (less than or equal to), it includes the boundary line itself. Therefore, the boundary line is solid, not dashed.
3. Shading the region:
- The inequality states [tex]\( y \leq -2x + 3 \)[/tex], which means the region where [tex]\( y \)[/tex] is less than or equal to [tex]\( -2x + 3 \)[/tex] needs to be shaded.
- This means that the area below the line [tex]\( y = -2x + 3 \)[/tex] on the graph will be shaded.
Given these steps, the correct description for the graph of the inequality [tex]\( y \leq -2x + 3 \)[/tex] is:
- The region shaded below a solid boundary line.
Thus, the correct option is:
The region shaded below a solid boundary line.
