Example 1: Graph the linear inequality y>2x-1y>2x−1.
The first thing is to make sure that variable yy is by itself on the left side of the inequality symbol, which is the case in this problem. Next is to graph the boundary line by momentarily changing the inequality symbol to equality symbol.
PICTURE
Graph the line y>2x-1y>2x−1 in the xy axis using your preferred method. Since the inequality symbol is just greater than “>” , and not greater than or equal to “≥“, the boundary line is dotted or dashed. So here’s how it should look so far.
PICTURE
The last step is to shade either above or below the boundary line. From the suggested steps, we were told to shade the top side of the boundary line if we have the inequality symbols > (greater than) or ≥ (greater than or equal to). Always remember that “greater than” implies “top”.
PICTURE
To check if your final graph of the inequality is correct, we can pick any points in the shaded region. For this, let’s have the point (−1, 1)
PICTURE
Evaluate the xx and yy values of the point into the inequality, and see if the statement is true. In the point (−1,1), the values are x=-1x=−1 and y=1y=1.
PICTURE
since x=-1 and y=1, we have y>2x-1 implies 1>2(-1)-1, 1>-3 which is true
Since the test point from the shaded region yields a true statement after checking with the original inequality, this shows that our final graph is correct!
Answers & Comments
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Examples of Graphing Linear Inequalities
Example 1: Graph the linear inequality y>2x-1y>2x−1.
The first thing is to make sure that variable yy is by itself on the left side of the inequality symbol, which is the case in this problem. Next is to graph the boundary line by momentarily changing the inequality symbol to equality symbol.
Graph the line y>2x-1y>2x−1 in the xy axis using your preferred method. Since the inequality symbol is just greater than “>” , and not greater than or equal to “≥“, the boundary line is dotted or dashed. So here’s how it should look so far.
The last step is to shade either above or below the boundary line. From the suggested steps, we were told to shade the top side of the boundary line if we have the inequality symbols > (greater than) or ≥ (greater than or equal to). Always remember that “greater than” implies “top”.
To check if your final graph of the inequality is correct, we can pick any points in the shaded region. For this, let’s have the point (−1, 1)
Evaluate the xx and yy values of the point into the inequality, and see if the statement is true. In the point (−1,1), the values are x=-1x=−1 and y=1y=1.
since x=-1 and y=1, we have y>2x-1 implies 1>2(-1)-1, 1>-3 which is true
Since the test point from the shaded region yields a true statement after checking with the original inequality, this shows that our final graph is correct!
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