To determine the correct graph for the boundary line of the inequality [tex]\( y \leq 2x - 4 \)[/tex], follow these steps:
1. Understand the Inequality: The inequality [tex]\( y \leq 2x - 4 \)[/tex] means that the region of interest is below or on the line described by the equation [tex]\( y = 2x - 4 \)[/tex].
2. Graph the Boundary Line: The boundary line is obtained by turning the inequality into an equation. So, we graph [tex]\( y = 2x - 4 \)[/tex].
3. Identify the Type of Line: Since the inequality is "less than or equal to" ( [tex]\( \leq \)[/tex] ), the boundary line will be solid. This indicates that points on the line [tex]\( y = 2x - 4 \)[/tex] are included in the solution set.
4. Plot Key Points:
- To plot [tex]\( y = 2x - 4 \)[/tex], use any two points to draw the line.
- Set [tex]\( x = 0 \)[/tex]: Then [tex]\( y = 2(0) - 4 = -4 \)[/tex]. So, one point is [tex]\( (0, -4) \)[/tex].
- Set [tex]\( x = 2 \)[/tex]: Then [tex]\( y = 2(2) - 4 = 0 \)[/tex]. So, another point is [tex]\( (2, 0) \)[/tex].
5. Draw the Line: Connect the points [tex]\( (0, -4) \)[/tex] and [tex]\( (2, 0) \)[/tex] with a solid line.
6. Shade the Region: Since [tex]\( y \leq 2x - 4 \)[/tex], shade the region below the line, including the line itself.
Final Decision: Select the option that displays a solid line through points (0, -4) and (2, 0), and the area below the line is shaded.
Given that the exact graphs aren't provided here, you should now look for a graph which meets all criteria detailed. This is how you identify the correct graph for the inequality [tex]\( y \leq 2x - 4 \)[/tex].
