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Verify the graph of the boundary line and the shaded region for each inequality.
Error:The incorrect regions are shaded for both inequalities.
Correction:
To find the error in this exercise we should attempt to verify the graph of the boundary line and the shaded region for each inequality one at a time.
Let's begin with examining the given system. y ≤ x-1 & (I) y ≥ x+3 & (II) Inequality (I): From the inequality we see that the boundary line should have a slope of 1 and a y-intercept of - 1. Since the symbol is ≤, the line should be solid.
Inequality (II): From the inequality we see that the boundary line should have a slope of 1 and a y-intercept of 3. Since the symbol is ≥, the line should be solid. We have drawn the graph below and added labels to make it easier to describe them.Examining the graph, we can see that both boundary lines have been graphed correctly.
x= 0, y= 0
Subtract terms
x= 0, y= 0
Add terms
The correct graph is shown below. We have used the boundary lines and shaded regions as described above.