To model the graph of the dotted line given by the equation \( y = -\frac{2}{3}x + 1 \) with a shaded region below the line, we need to express this relationship as a linear inequality.
The equation of the line is in slope-intercept form \( y = mx + b \), where \( m = -\frac{2}{3} \) and \( b = 1 \). Since the line is dotted, it indicates that points on the line are not included in the solution set, which corresponds to using a "less than" inequality.
Since the region is shaded below the line, we are looking for points where \( y \) is less than the value of \( y \) given by the line equation. Therefore, we can write the inequality as:
\[ y < -\frac{2}{3}x + 1 \]
This inequality models the graph of the dotted line with the shaded region below it.