Lesson 14: Using Linear Relations to Solve Problems | Unit 3: Linear Relationships

Multiple Select

Select **all** the situations for which only zero or positive solutions make sense.

• The height of a candle as it burns over an hour.

• The number of students remaining in school after 6:00 p.m.

• Measuring temperature in degrees Celsius at an Arctic outpost each day in January.

• A bank account balance over a year.

• The elevation above sea level of a hiker descending into a canyon.

Open Ended

The owner of a new restaurant is ordering tables and chairs. He wants to have only tables for 2 and tables for 4. The total number of people that can be seated in the restaurant is 120. Describe some possible combinations of 2-seat tables and 4-seat tables that will seat 120 customers. Explain how you found them.

Multiple Choice

The owner of a new restaurant is ordering tables and chairs. He wants to have only tables for 2 and tables for 4. The total number of people that can be seated in the restaurant is 120. Let $$x$$ represent the number of 2-seat tables and $$y$$ represent the number of 4-seat tables. Which equation represents the situation?

• 2x + 3y = 120
• 3x + 4y = 120
• x + 2y = 120
• 2x + 4y = 120

Draw

The owner of a new restaurant is ordering tables and chairs. He wants to have only tables for 2 and tables for 4. The total number of people that can be seated in the restaurant is 120. Create a graph to represent the situation.

Multiple Choice

The owner of a new restaurant is ordering tables and chairs. He wants to have only tables for 2 and tables for 4. The total number of people that can be seated in the restaurant is 120. What does the slope tell us about the situation?

• The slope indicates the rate of change in seating capacity per table type.
• The slope indicates the number of chairs needed per table.
• The slope shows the maximum capacity of the restaurant.
• The slope represents the total number of tables ordered.

Multiple Choice

The owner of a new restaurant is ordering tables and chairs. He wants to have only tables for 2 and tables for 4. The total number of people that can be seated in the restaurant is 120. Interpret the $$x$$ and $$y$$ intercepts in the situation.

• The x-intercept represents the maximum number of tables for 2 (60), and the y-intercept represents the maximum number of tables for 4 (30).
• The x-intercept represents the maximum number of tables for 4 (60), and the y-intercept represents the maximum number of tables for 2 (30).
• The x-intercept represents the total number of chairs (120), and the y-intercept represents the total number of tables (30).
• The x-intercept represents the number of people that can be seated at tables for 2 (30), and the y-intercept represents the number of people that can be seated at tables for 4 (60).