To model the graph of the solid line \( y = 2x - 4 \) with a shaded region above the line, you need to write a linear inequality that represents all points above that line.
Since the line is given as \( y = 2x - 4 \), the inequality that describes the shaded region above this line is:
\[ y > 2x - 4 \]
This inequality includes all the points above the solid line, excluding the line itself, since it is an open inequality.
However, since the line is solid, the line itself is included in the solution set. Therefore, the correct inequality that includes the line itself would be:
\[ y \geq 2x - 4 \]
Though this option is not provided, from the given options, the best representation of the graph with shading above the line would be:
a. \( y > 2x - 4 \)
If we need a strict inequality without including the points on the line, this would be the correct choice. If you want to include the line itself, then \( y \geq 2x - 4 \) is the preferred option, which is not provided here.
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