GRAPHING LINEAR INEQUALITIES IN TWO VARIABLES WORKSHEET

Graph the solutions to each of the following inequalities on a separate set of axes.

Problem 1 :

y ≤ 3x + 1

Solution

Problem 2 :

y ≥ -2x + 3

Solution

Problem 3 :

y > 4x - 2

Solution

Problem 4 :

y < -3x - 5

Solution

Problem 5 :

y ≤ 3

Solution

Problem 6 :

x > 1

Solution

Problem 7 :

y > 2/3x + 8

Solution

Problem 8 :

You have two part-time summer jobs, one that pays $9 an hour and another that pays $12 an hour. You would like to earn at least $240 a week. Write an inequality describing the possible amounts of time you can schedule at both jobs.

Solution

Problem 9 :

The graph of an inequality is shown below.

a) Write the inequality represented by the graph.

b) On the same set of axes, graph the inequality x + 2y < 4

c) The two inequalities graphed on the set of axes form a system. Oscar thinks that  (2, 1) the point is in the solution set for this system of inequalities. Determine and state whether you agree with Oscar. Explain your reasoning.

Solution

Answer Key

1)  

2)  

3)

4) 

5) 

6) 

7) 

8) 

9) a)  the inequality represented by the graph is y ≥ 2x - 3.

c) (2, 1) is the point of intersection of the inequality. So, it must be a solution.

Graph the solutions to each of the following inequalities on a separate set of axes.

Problem 1 :

y < -3/5x - 7

Solution

Problem 2 :

3x + 2y ≥ 7

Solution

Problem 3 :

-4x + 2y < 3

Solution

Problem 4 :

Given x + y > 2

y ≤ 3x - 2

Which graph shows the solutions of the given set of inequalities ?

Solution

Problem 5 :

An online store sells digital cameras and cell phones. The store makes a $100 profit on the sale of each digital camera x and a $50 profit on the sale of each cell phone y. The store wants to make a profit of at least $300 from its sales of digital cameras and cell phones. Write and graph an inequality that represents how many digital cameras and cell phones they must sell. Identify and interpret two solutions of the inequality.

Solution

Problem 6 :

Write an inequality that represents the graph.

Solution

Answer Key

1) x -intercept:  (-35/3, 0) and y -intercept:  (0, -7)

2) x -intercept:  (7/3, 0) and y -intercept:  (0, 7/2)

3) x -intercept:  (-3/4, 0) and y -intercept:  (0, 3/2)

4) option 2

5) 

6) the inequality represented by the graph is y > (1/2) x - 2.

Problem 1 :

Katie has $50 in a savings account at the beginning of the summer. She wants to have at least $20 in the account by the end of the summer. She withdraws $2 each week for food, clothes, and movie tickets. Write an inequality that expresses Katie’s situation and display it on the graph below. For how many weeks can Katie withdraw money?

Solution

Problem 2 :

Skate Land charges a $50 flat fee for a birthday party rental and $4 for each person. Joann has no more than $100 to budget for her party. Write an inequality that models her situation and display it on the graph below. How many people can attend Joann's party.

Solution

Problem 3 :

Sarah is selling bracelets and earrings to make money for summer vacation. The bracelets cost $2 and the earrings cost $3. She needs to make at least $60. Sarah knows she will sell more than 10 bracelets. Write inequalities to represent the income from jewelry sold and number of bracelets sold. Find two possible solutions. 

Solution

Problem 4 :

An online store sells digital cameras and cell phones. The store makes a $100 profit on the sale of each digital camera x and a $50 profit on the sale of each cell phone y. The store wants to make a profit of at least $300 from its sales of digital cameras and cell phones. Write and graph an inequality that represents how many digital cameras and cell phones they must sell. Identify and interpret two solutions of the inequality.

Solution

Problem 5 :

The Reel Good Cinema is conducting a mathematical study. In its theater, there are 200 seats. Adult tickets cost $12.50 and child tickets cost $6.25. The cinema's goal is to sell at least $1500 worth of tickets for the theater. Write a system of linear inequalities that can be used to find the possible combinations of adult tickets, x, and child tickets, y, that would satisfy the cinema's goal. Graph the solution to this system of inequalities on the set of axes below. Label the solution with an S. Marta claims that selling 30 adult tickets and 80 child tickets will result in meeting the cinema's goal. Explain whether she is correct or incorrect, based on the graph drawn.

Solution

Answer Key

1)

2) x ≤ 12.5

3) The two possible solutions are 

x = 12 and y = 12 

x = 15 and y = 10

4)

• To have the profit more than $300 the store have to sale 4 cameras and 4 cell phones
• To have the profit more than $300 the store have to sale 6 cameras and 6 cell phones

5) 

Adult tickets = 30

Child tickets = 80

is not a solution.