Practice Makes Perfect
Verify Solutions to an Inequality in Two Variables
In the following exercises, determine whether each ordered pair is a solution to the given inequality.
Exercise \(\PageIndex{1}\)
Determine whether each ordered pair is a solution to the inequality \(y>x−1\):
 \((0,1)\)
 \((−4,−1)\)
 \((4,2)\)
 \((3,0)\)
 \((−2,−3)\)
Exercise \(\PageIndex{2}\)
Determine whether each ordered pair is a solution to the inequality \(y>x−3\):
 \((0,0)\)
 \((2,1)\)
 \((−1,−5)\)
 \((−6,−3)\)
 \((1,0)\)
 Answer

 yes
 no
 no
 yes
 no
Exercise \(\PageIndex{3}\)
Determine whether each ordered pair is a solution to the inequality \(y<x+2\):
 \((0,3)\)
 \((−3,−2)\)
 \((−2,0)\)
 \((0,0)\)
 \((−1,4)\)
Exercise \(\PageIndex{4}\)
Determine whether each ordered pair is a solution to the inequality \(y<x+5\):
 \((−3,0)\)
 \((1,6)\)
 \((−6,−2)\)
 \((0,1)\)
 \((5,−4)\)
 Answer

 yes
 no
 no
 yes
 yes
Exercise \(\PageIndex{5}\)
Determine whether each ordered pair is a solution to the inequality \(x+y>4\):
 \((5,1)\)
 \((−2,6)\)
 \((3,2)\)
 \((10,−5)\)
 \((0,0)\)
Exercise \(\PageIndex{6}\)
Determine whether each ordered pair is a solution to the inequality \(x+y>2\):
 \((1,1)\)
 \((4,−3)\)
 \((0,0)\)
 \((−8,12)\)
 \((3,0)\)
 Answer

 no
 no
 no
 yes
 yes
Recognize the Relation Between the Solutions of an Inequality and its Graph
In the following exercises, write the inequality shown by the shaded region.
Exercise \(\PageIndex{7}\)
Write the inequality shown by the graph with the boundary line \(y=3x−4\).

Exercise \(\PageIndex{8}\)
Write the inequality shown by the graph with the boundary line \(y=2x−4\).
 Answer

\(y<2 x4\)
Exercise \(\PageIndex{9}\)
Write the inequality shown by the graph with the boundary line \(y=\frac{1}{2} x+1\)
Exercise \(\PageIndex{10}\)
Write the inequality shown by the graph with the boundary line \(y=\frac{1}{3} x2\)
 Answer

\(y \leq\frac{1}{3} x2\)
Exercise \(\PageIndex{11}\)
Write the inequality shown by the shaded region in the graph with the boundary line \(x+y=5\).
Exercise \(\PageIndex{12}\)
Write the inequality shown by the shaded region in the graph with the boundary line \(x+y=3\).
 Answer

\(x+y \geq 3\)
Exercise \(\PageIndex{13}\)
Write the inequality shown by the shaded region in the graph with the boundary line \(2x+y=−4\).

Exercise \(\PageIndex{14}\)
Write the inequality shown by the shaded region in the graph with the boundary line \(x+2y=−2\).
 Answer

\(x+2 y \geq2\)
Exercise \(\PageIndex{15}\)
Write the inequality shown by the shaded region in the graph with the boundary line \(3x−y=6\).

Exercise \(\PageIndex{16}\)
Write the inequality shown by the shaded region in the graph with the boundary line \(2x−y=4\).
 Answer

\(2 xy<4\)
Exercise \(\PageIndex{17}\)
Write the inequality shown by the shaded region in the graph with the boundary line \(2x−5y=10\).

Exercise \(\PageIndex{18}\)
Write the inequality shown by the shaded region in the graph with the boundary line \(4x−3y=12\).
 Answer

\(4 x3 y>12\)
Graph Linear Inequalities
In the following exercises, graph each linear inequality.
Exercise \(\PageIndex{19}\)
Graph the linear inequality \(y>\frac{2}{3} x1\)
Exercise \(\PageIndex{20}\)
Graph the linear inequality \(y<\frac{3}{5} x+2\)
 Answer

Exercise \(\PageIndex{21}\)
Graph the linear inequality \(y \leq\frac{1}{2} x+4\)
Exercise \(\PageIndex{22}\)
Graph the linear inequality \(y \geq\frac{1}{3} x2\)
 Answer

Exercise \(\PageIndex{23}\)
Graph the linear inequality \(xy \leq 3\)
Exercise \(\PageIndex{24}\)
Graph the linear inequality \(xy \geq 2\)
 Answer

Exercise \(\PageIndex{25}\)
Graph the linear inequality \(4x+y>4\)
Exercise \(\PageIndex{26}\)
Graph the linear inequality \(x+5y<5\)
 Answer

Exercise \(\PageIndex{27}\)
Graph the linear inequality \(3 x+2 y \geq6\)
Exercise \(\PageIndex{28}\)
Graph the linear inequality \(4 x+2 y \geq8\)
 Answer

Exercise \(\PageIndex{29}\)
Graph the linear inequality \(y>4x\)
Exercise \(\PageIndex{30}\)
Graph the linear inequality \(y>x\)
 Answer

Exercise \(\PageIndex{31}\)
Graph the linear inequality \(y \leqx\)
Exercise \(\PageIndex{32}\)
Graph the linear inequality \(y \leq3 x\)
 Answer

Exercise \(\PageIndex{33}\)
Graph the linear inequality \(y \geq2\)
Exercise \(\PageIndex{34}\)
Graph the linear inequality \(y<1\)
 Answer

Exercise \(\PageIndex{35}\)
Graph the linear inequality \(y<4\)
Exercise \(\PageIndex{36}\)
Graph the linear inequality \(y \geq 2\)
 Answer

Exercise \(\PageIndex{37}\)
Graph the linear inequality \(x \leq 5\)
Exercise \(\PageIndex{38}\)
Graph the linear inequality \(x>2\)
 Answer

Exercise \(\PageIndex{39}\)
Graph the linear inequality \(x>3\)
Exercise \(\PageIndex{40}\)
Graph the linear inequality \(x \leq 4\)
 Answer

Exercise \(\PageIndex{41}\)
Graph the linear inequality \(xy<4\)
Exercise \(\PageIndex{42}\)
Graph the linear inequality \(xy<3\)
 Answer

Exercise \(\PageIndex{43}\)
Graph the linear inequality \(y \geq \frac{3}{2} x\)
Exercise \(\PageIndex{44}\)
Graph the linear inequality \(y \leq \frac{5}{4} x\)
 Answer

Exercise \(\PageIndex{45}\)
Graph the linear inequality \(y>2 x+1\)
Exercise \(\PageIndex{46}\)
Graph the linear inequality \(y<3 x4\)
 Answer

Exercise \(\PageIndex{47}\)
Graph the linear inequality \(x \leq1\)
Exercise \(\PageIndex{48}\)
Graph the linear inequality \(x \geq 0\)
 Answer
