First, we have to find the equation of the dotted line.
The slope of the line that passes through the points (x1, y1) and (x2, y2) is computed as follows:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
The line passes through the points (0,2) and (2, 3), then its slope is:
[tex]m=\frac{3-2}{2-0}=\frac{1}{2}[/tex]
The slope-intercept form of a line is:
y = mx + b
where m is the slope and b is the y-intercept.
Since the line intersects the y-axis at (0,2), b = 2. Then the equation of the line is:
y = 1/2x + 2
Given that the shaded region is above the dotted line, the inequality is:
y > 1/2x + 2
