Graph Linear Inequalities Worksheet

**Page 2**

11.

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.]

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)

12.

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 (>), use dashed line to represent the boundary of

0 > 0 + 4

0 > 4

Test a point not on the boundary line.

Test (0, 0) in the inequality.

[Substitute.]

[False.]

Since the inequality is false for (0, 0), shade the region that does not contain (0, 0).

The above graph matches with the graph 3.

Correct answer : (3)

13.

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.]

[True.]

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)

14.

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.]

[True.]

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

The above graph matches graph 3.

Correct answer : (3)

15.

Which of the graphs represent the linear inequality $y$ ≥ 5$x$ - 3?

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 - 3

0 ≥ -3

Test a point not on the boundary line.

Test (0, 0) in the inequality.

[Substitute.]

[True.]

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

The above graph matches with Graph 1.

Correct answer : (1)

16.

Write the linear inequality for the graph.

a. | 6$x$ - 3$y$ ≤ 12 | ||

b. | 6$x$ - 3$y$ ≥ 12 | ||

c. | -6$x$ + 3$y$ ≥ 12 | ||

d. | 6$x$ + 3$y$ ≤ -12 |

Take a point from the shaded region i.e. solution and check which of the equations satisfies the linear inequality.

6(3) - 3(1) ≥ 12

15 ≥ 12

[Replace

[True.]

The linear inequality for the graph is 6

Correct answer : (2)

17.

Write the equation of the boundary line 5$x$ + 6$y$ ≤ 18, in slope-intercept form.

a. | y = $\frac{-5}{18}$x - 3 | ||

b. | y = $\frac{5}{6}$x - 3 | ||

c. | x = $\frac{-5}{6}$y + 3 | ||

d. | y = $\frac{-5}{6}$x + 3 |

[Original equation.]

5

[Write the inequality in the form of equality.]

6

[Add -5

[To write in slope-intercept form divide each side by 6.]

The equation of the boundary line in slope - intercept form is

Correct answer : (4)

18.

Write a system of linear inequalities to describe the graph.

a. | y ≤ $\frac{3}{2}$x + 3; y ≥ -x - 3 | ||

b. | y ≥ $\frac{-3}{2}$x - 3; y ≤ -x + 3 | ||

c. | y ≥ $\frac{3}{2}$x + 3; y > -x + 3 | ||

d. | y ≤ $\frac{3}{2}$x + 3; y > -x + 3 |

[From the graph.]

The equation of Line 1 in slope-intercept form is

[Substitute

As Line 1 is a solid line and the region above the line is shaded, the equation should be

[From the graph.]

The

[From the graph.]

The equation of Line 2 in slope-intercept form is

[Substitute

As Line 2 is a dashed line and the region above the line is shaded, the inequality should be

[From the graph.]

So, the system of linear inequalities is

Correct answer : (3)

19.

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)

20.

Write a system of linear inequalities to describe the graph.

a. | y < $\frac{2}{3}$x + 1; y > -x - 3 | ||

b. | y > $\frac{2}{3}$x + 2; y ≤ -x - 3 | ||

c. | y < $\frac{2}{3}$x + 2; y ≥ -x - 3 | ||

d. | y < $\frac{2}{3}$x + 1; y ≤ -x - 3 |

[From the graph.]

The equation of Line 1 in slope-intercept form is

[Substitute

As Line 1 is a dashed line and the region above the line is shaded, the equation should be

[From the graph.]

The

[From the graph.]

The equation of Line 2 in the slope-intercept form is

[Substitute

As Line 2 is a solid line and the region below the line is shaded, the inequality should be

[From the graph.]

So, the system of linear inequalities is

Correct answer : (2)