Graph Linear Inequalities Worksheet

**Page 1**

1.

Which of the graphs represents the inequality? $y$ < $x$ + 4

a. | Graph 1 | ||

b. | Graph 2 | ||

c. | Graph 3 | ||

d. | Graph 4 |

Since the inequality involves less than (<), use dashed line to represent the boundary of

0 < 0 + 4

0 < 4 True

Test a point not on the boundary line.

Test (0, 0) in the inequality.

[Substitute the values.]

Since the inequality is true for (0, 0), shade the region containing (0, 0).

The above graph matches with the graph 2.

Correct answer : (2)

2.

Which of the graphs, represents the inequality? $y$ ≥ $x$ - 4

a. | Graph 1 | ||

b. | Graph 2 | ||

c. | Graph 3 | ||

d. | Graph 4 |

Since the inequality involves greater than or equal to (≥), the boundary line of the inequality

0 ≥ 0 - 4

0 ≥ - 4

Test a point not on the boundary line.

Test (0, 0) in the inequality.

[Substitute the values.]

Since the inequality is true for (0, 0), shade the region that contains (0, 0).

The above graph matches with the graph 4.

Correct answer : (4)

3.

Graph the system of linear inequalities.

$x$ ≥ 0

$y$ ≥ 0

4$x$ + 6$y$ ≤ 12

a. | Graph 1 | ||

b. | Graph 2 | ||

c. | Graph 3 | ||

d. | Graph 4 |

The graph of

The graph of

The graph of 4

The shaded portion shown below is the intersection of the three half-planes, which is the graph of the system.

So, Graph 1 represents the system of linear inequalities.

Correct answer : (1)

4.

Which of the graphs represents the inequality $x$ - $y$ > - 1?

a. | Graph 2 | ||

b. | Graph 1 | ||

c. | Both A and B | ||

d. | None of the above |

[Write corresponding equation].

[Subtracting

The corresponding equation in slope-intercept form is

The graph of the line has a slope of 1 and a

The point (0, 0) satisfies the inequality. So, the solution is the half of the plane that includes the point (0, 0).

Correct answer : (2)

5.

Find the two numbers whose difference is less than or equal to 5. Show the solution by graphing an inequality.

a. | Graph 1 | ||

b. | Graph 2 | ||

c. | Graph 3 | ||

d. | Graph 4 |

[The difference of the two numbers is less than or equal to 5.]

Since the inequality involves less than or equal to(≤) the boundary line of the equation

Substitute any point in the equation that does not lie on the boundary line.

2 - 1 ≤ 5

[Test (2, 1).]

1 ≤ 5

[True.]

The inequality 1 ≤ 5 is true. So, shade the region that contains (2, 1) as shown

The above graph matches with the graph 2.

Correct answer : (2)

6.

Graph the linear inequality: |$x$| ≥ 3

a. | Graph C | ||

b. | Graph A | ||

c. | Graph B | ||

d. | Graph D |

The graph of |

Correct answer : (1)

7.

Check whether the ordered pair (0, $\frac{-6}{5}$ ) is a solution of the inequality 4$x$ + 5$y$ ≤ 4 .

a. | No | ||

b. | Yes |

4

[Take left hand side of the inequality.]

= 4(0) + 5(

[Substitute the values.]

= 0 + (-6)

[Simplify.]

-6 ≤ 4

[Compare with the right hand side of the orginal expression.]

The ordered pair is a solution of 4

Correct answer : (2)

8.

Which of the graphs represents the inequality? $y$ ≤ 5$x$ + 3

a. | Graph 1 | ||

b. | Graph 2 | ||

c. | Graph 3 | ||

d. | Graph 4 |

Since the inequality involves less than or equal to (≤), the boundary line of the inequality

0 ≤ 0 + 3

0 ≤ 3

Test a point not on the boundary line.

Test (0, 0) in the inequality.

[Substitute the values.]

Since the inequality is true for (0, 0), shade the region that contains (0, 0).

The above graph matches graph 3.

Correct answer : (3)

9.

Graph the system of linear inequalities.

2$x$ - 3$y$ < 6

- $x$ + $y$ ≤ 4

2$x$ + 4$y$ < 8

a. | Graph 1 | ||

b. | Graph 2 |

The graph of -

The graph of 2

Finally, the graph of the system is the intersection of the three half-plane as shown in the graph.

Correct answer : (2)

10.

Which of the graphs best represents the system of inequalities, $x$ + $y$ < 3 , - 5$x$ + 2$y$ ≤ 10 , $y$ ≥ - 3?

a. | Graph 1 | ||

b. | Graph 3 | ||

c. | Graph 4 | ||

d. | Graph 2 |

Graph all the three inequalitites in the same coordinate plane.

The graph of

The graph of - 5

The graph of

The graph of the system is the intersection of the three half planes as shown in the graph.

Graph 1 is the correct answer.

Correct answer : (1)