Linear Models and Rate of Change

This lesson focuses on graphing lines specified by linear functions. It includes examples such as a truck rental cost model, car depreciation over time, and book sales based on pricing. The lesson emphasizes understanding rate of change and initial values in linear functions, and how to graph these relationships. Students are encouraged to practice with exercises to reinforce their understanding.

What is the primary focus of the lesson on graphing lines?

• Graphing quadratic functions

• Graphing lines using linear functions

• Graphing exponential functions

• Graphing polynomial functions

In the truck rental example, what is the initial cost when no miles are driven?

• $0

• $100

• $150

• $50

How much does the truck rental cost increase per mile driven?

• $1.50

• $0.25

• $0.50

• $1.00

What is the rate of change in the car depreciation example?

• -$2500 per year

• -$2000 per year

• -$1500 per year

• -$1000 per year

After how many years does the car's value reach $500?

• 7 years

• 6 years

• 8 years

• 5 years

In the book pricing example, how many copies are sold if the book is priced at $15?

• 400 copies

• 600 copies

• 800 copies

• 1000 copies

What is the rate of change in the number of books sold per $1 increase in price?

• -30 books

• -40 books

• -50 books

• -60 books

If the book is priced at $18, how many copies are expected to be sold?

• 550 copies

• 650 copies

• 850 copies

• 750 copies

What happens to the car's value in the model after 7 years?

• It increases

• It remains constant

• It becomes negative

• It becomes zero

Why might a linear model not be suitable for all values of a variable?

• Because it is too complex

• Because it requires a quadratic relationship

• Because it only works for positive values

• Because it assumes a constant rate of change