Understanding Linear Functions in Real-Life Scenarios

The video tutorial explains how to model a real-world problem using a linear function. It starts with a scenario involving a $180 gift card for gas, with $16 spent weekly. The tutorial covers the basics of linear functions, including slope and intercept, and formulates a function to represent the remaining balance on the card over time. It concludes by evaluating the function for a specific week to determine the remaining balance.

What is the initial value of the gift card?

• $180

• $150

• $100

• $200

How much is spent on gas per week?

• $20

• $10

• $18

• $16

What does the slope represent in a linear function?

• The initial value

• The rate of change

• The maximum value

• The minimum value

In the function G(w) = -16w + 180, what does the number 180 represent?

• The final amount

• The initial amount

• The weekly spending

• The slope

What is the correct form of the linear function for this problem?

• G(w) = -180 + 16w

• G(w) = 180 + 16w

• G(w) = 180 - 16w

• G(w) = 16w + 180

If the weekly spending increased to $20, what would be the new slope?

• -20

• -16

• -18

• -22

How do you calculate the remaining value on the card after 6 weeks?

• Subtract $96 from the initial value

• Add $16 to the initial value

• Multiply $16 by 6

• Divide $180 by 6

What is the remaining value on the card after 6 weeks?

• $124

• $64

• $84

• $104

What does the function value G(6) = 84 indicate?

• The card has $84 remaining after 8 weeks

• The card has $84 remaining after 6 weeks

• The card has $16 remaining after 6 weeks

• The card is fully used

What is the purpose of evaluating G(6) in this context?

• To find the total amount spent

• To calculate the initial value

• To find the weekly spending

• To determine the remaining balance after 6 weeks