Final answer:
The correct statement about the inequality graphed here is that (2,1) does NOT fall in the shaded region.
Step-by-step explanation:
The correct answer is C) (2,1) falls in the shaded region. In the graph, the shaded region represents the solution set of the inequality, which is the set of all points that satisfy the inequality. The point (2,1) falls in the shaded region, so the statement is correct.
To determine the slope of the line, we can rewrite the inequality in slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept. The given inequality is y < -x + 2, which can be rewritten as y = -x + 2. The slope is negative, as indicated by the negative coefficient of x.
The dotted line represents the boundary of the solution set. The equation of the dotted line is y = -x + 2, which is the same as the equation of the inequality in slope-intercept form. So, the statement D) The dotted line has the equation y = -x + 2 is also correct.
Therefore, the only statement that is incorrect is C) (2,1) falls in the shaded region.