Graphing Linear Inequalities in Two Variables Worksheet

**Page 2**

11.

Choose the ordered pair which is the solution for the inequality 4$x$ + 5$y$ ≤ 0.

a. | (0, $\frac{6}{5}$) | ||

b. | (0, - $\frac{6}{5}$) | ||

c. | (6, - $\frac{6}{5}$) | ||

d. | (- 1, $\frac{6}{5}$) |

[Original inequality.]

4(0) + 5(-

[Replace

- 6 ≤ 0, which is true

[Subtract.]

4(0) + 5(

[Replace

6 ≤ 0, which is false

[Subtract.]

4(6) + 5(-

[Replace

18 ≤ 0, which is false

[Subtract.]

4(- 1) + 5(

[Replace

2 ≤ 0, which is false

[Subtract.]

So, the ordered pair (0, -

Correct answer : (2)

12.

Choose 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 that is 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)

13.

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

a. | $y$ = - $\frac{5}{6}$$x$ + 9 | ||

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

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

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

[Original inequality.]

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 : (2)

14.

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)

15.

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)

16.

Write the equation of the boundary line 2$x$ + 5$y$ ≥ 10 in slope-intercept form.

a. | $y$ = $\frac{2}{5}$$x$ - 2 | ||

b. | $y$ = $\frac{2}{5}$$x$ + 2 | ||

c. | $y$ = - $\frac{2}{5}$$x$ - 2 | ||

d. | $y$ = - $\frac{2}{5}$$x$ + 2 |

[Original inequality.]

2

[Write the inequality in the form of equality.]

5

[Add - 2

[To write in slope-intercept form divide both sides by 5.]

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

Correct answer : (4)

17.

Write the equation of the boundary line 2$x$ - 3$y$ ≥ 6 in slope-intercept form.

a. | $y$ = ($\frac{2}{3}$)$x$ - 2 | ||

b. | $y$ = - ($\frac{2}{3}$)$x$ + 2 | ||

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

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

[Original inequality.]

2

[Write the inequality in the form of equality.]

- 3

[Add - 2

3

[Multiply with - 1 on both sides.]

[Divide by 3 on each side.]

Correct answer : (1)

18.

Which of the following inequalities the boundary line in the graph would be solid?6

a. | 4$x$ + 5$y$ > 3 | ||

b. | 5$x$ - 6$y$ < 2 | ||

c. | 4$x$ + 5$y$ < 3 | ||

d. | 5$x$ + 6$y$ ≥ 2 |

For the inequalities 4

For the inequality 5

Correct answer : (4)

19.

Which of the following inequalities the boundary line in the graph would be dashed?

a. | 9$x$ + 10$y$ ≤ 3 | ||

b. | 9$x$ - $y$ ≥ 3 | ||

c. | $x$ + 9$y$ ≤ 3 | ||

d. | 9$x$ + $y$ > 3 |

For the inequalities 9

For the inequality 9

Correct answer : (4)