Graph Linear Inequalities Worksheet

**Page 3**

21.

Write a system of linear inequalities to describe the graph.

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

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

c. | y > x + 1; y ≤ $\frac{2}{3}$x + 2 | ||

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

[From the graph.]

The equation of Line 1 in slope-intercept form is

[Substitute

As Line 1 is a dashed line and the region below 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 equation should be

[From the graph.]

So, the system of inequalities is

Correct answer : (4)

22.

Which of the inequalities represents 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 |

The equation of the line in slope-intercept form is

[Substitute

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

3

[Multiply by 3 on both sides of inequality.]

6

[Rearrange the inequality.]

So, 6

Correct answer : (4)

23.

Which of the inequalities represents 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 |

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

[Substitute

As the boundary line is a dotted line and the side not containing the origin is shaded the inequality should be

3

[Multiply the above inequality by 3.]

-6

[Rearrange the above inequality.]

So, the inequality -6

Correct answer : (4)

24.

Write the equation of the boundary line -4$x$ + 7$y$ ≤ 28 in slope-intercept form.

a. | y = -($\frac{4}{7}$)x - 4 | ||

b. | y = ($\frac{4}{7}$)x + 4 | ||

c. | y = -($\frac{4}{7}$)x + 4 | ||

d. | y = ($\frac{4}{7}$)x - 4 |

[Original equation.]

-4

[Write the inequality in form of equality.]

7

[Add 4

[Divide by 7 on each side.]

Correct answer : (2)

25.

Write the equation of the boundary line 3$x$ + 7$y$ ≥ 14 in slope-intercept form.

a. | y = $\frac{-3}{7}$x + 2 | ||

b. | $y$ = $\frac{3}{7}$$x$ - 2 | ||

c. | y = $\frac{-3}{7}$x - 2 | ||

d. | y = $\frac{3}{7}$x + 2 |

[Original equation.]

3

[Write the inequality in the form of equality.]

7

[Add -3

[To write in slope-intercept form divide both sides by 7.]

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

Correct answer : (1)

26.

Write the equation of the boundary line 8$x$ - 9$y$ ≥ 45 in slope-intercept form.

a. | y = ($\frac{8}{9}$)x + 5 | ||

b. | y = -($\frac{8}{9}$)x + 5 | ||

c. | y = -($\frac{8}{9}$)x - 5 | ||

d. | y = ($\frac{8}{9}$)x - 5 |

[Original equation.]

8

[Write the inequality in the form of equality.]

9

[Add 9

[Divide by 9 on each side.]

Correct answer : (4)

27.

Tell whether the boundary line 7$x$ + $y$ ≥ 9 is solid or dashed.

a. | Dashed | ||

b. | Solid |

[Original Equation.]

If the points on the boundary line make 7

As the inequality involves greater than or equal to(≥) (7

So, the boundary line is a solid line.

Correct answer : (2)

28.

Tell whether the boundary line of the inequality 9$x$ + $y$ > 2 is solid or dashed.

a. | Solid | ||

b. | Dashed |

[Original Equation.]

If the points on the boundary line make 9

As the inequality involves '>', (9

So, the boundary line is a dashed line.

Correct answer : (2)