To model the graph of the dotted line given by the equation \( y = 7x - 4 \) with a shaded region above the line, we need to convert the equation of the line into an inequality.
Since the graph is a dotted line, it indicates that the line itself is not included in the solution set, which corresponds to the use of a "less than" or "greater than" symbol, rather than "less than or equal to" or "greater than or equal to."
Since the shaded region is above the line, we want all the points where \( y \) is greater than the value of \( y \) on the line. Therefore, the inequality can be expressed as:
\[ y > 7x - 4 \]
So, the linear inequality that models the graph of the dotted line \( y = 7x - 4 \) with a shaded region above the line is:
\[ y > 7x - 4 \]