Lesson 09: Linear Models | Unit 5: Functions and Volume

Multiple Choice

How many miles would a customer need to drive so that the monthly charge is $100?

• 30 miles
• 70 miles
• 50 miles
• 90 miles

Open Ended

A car sharing service charges your account once a month according to how much you use their cars. The graph shows the amount charged for the month in dollars as a function of the number of miles driven. Is the monthly charge a linear function of miles driven? Explain your reasoning.

Multiple Choice

In science class, Jada uses a graduated cylinder with water in it to measure the volume of some marbles. After dropping in 4 marbles so they are all under water, the water in the cylinder is at a height of 10 milliliters. After dropping in 6 marbles so they are all under water, the water in the cylinder is at a height of 11 milliliters. What is the volume of 1 marble?

• 2 milliliters
• 1 milliliter
• 0.5 milliliters
• 0.25 milliliters

Multiple Choice

In science class, Jada uses a graduated cylinder with water in it to measure the volume of some marbles. How much water was in the cylinder before any marbles were dropped in?

• Indeterminate based on the information provided.
• 100 mL
• 50 mL
• 10 mL

Multiple Choice

In science class, Jada uses a graduated cylinder with water in it to measure the volume of some marbles. What should the height of the water be after 13 marbles are dropped in?

• The water level will rise by exactly 5 cm.
• The height of the water will decrease after adding the marbles.
• The water will overflow immediately after adding the marbles.
• The height of the water will depend on the volume of the marbles and the initial water level.

Open Ended

In science class, Jada uses a graduated cylinder with water in it to measure the volume of some marbles. Is the relationship between volume of water and number of marbles a linear relationship? If so, what does the slope of a line representing this relationship mean? If not, explain your reasoning.

Open Ended

For a certain city, the graph shows the number of days after the new year on the horizontal axis and the high temperatures (in degrees Celsius) on the vertical axis. Based on this information, is the high temperature in this city a linear function of the number of days after the new year?

Open Ended

Lin’s smart phone was fully charged when she started school at 8:00 a.m. At 9:20 a.m., it was 90% charged, and at noon, it was 72% charged. When do you think her battery will be 0% charged? Explain your reasoning.

Open Ended

Lin’s smart phone was fully charged when she started school at 8:00 a.m. At 9:20 a.m., it was 90% charged, and at noon, it was 72% charged. Is battery life a function of time? If yes, is it a linear function? Explain your reasoning.

Open Ended

After almost running out of space on her phone, Elena checks with a couple of friends who have the same phone to see how many pictures they have on their phones and how much memory they take up. The results are shown in the table.

Could this information be reasonably modeled with a linear function? Explain your reasoning.