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

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.

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.

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?

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.

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.

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.