Understanding Linear Equations: Slope and Intercept Insights

1. A car rental company charges a flat fee of $20 plus $0.15 per mile driven. Write the linear equation that represents the total cost (C) in terms of miles driven (m). What is the slope and what does it represent in this context?

• C = 15 + 0.15m; slope = 0.15 (base fee)

• C = 20 + 0.15m; slope = 0.15 (cost per mile)

• C = 20 + 0.20m; slope = 0.20 (cost per mile)

• C = 20 + 0.10m; slope = 0.10 (cost per mile)

2. Sarah and Tom are saving money for a concert. Sarah saves $5 each week, while Tom saves $8 each week. Write the equations for the amount saved by each after w weeks. How do their savings compare after 4 weeks?

• After 4 weeks, Sarah has saved $20 and Tom has saved $32.

• After 4 weeks, Sarah has saved $25 and Tom has saved $40.

• After 4 weeks, Sarah has saved $10 and Tom has saved $20.

• After 4 weeks, Sarah has saved $15 and Tom has saved $24.

3. A phone company offers two plans: Plan A costs $30 per month with no additional fees, while Plan B costs $20 per month plus $10 for each gigabyte of data used. Write the equations for the total cost of each plan based on data usage (d). At what point do the costs of both plans become equal?

• 1 gigabyte

• 5 gigabytes

• 2 gigabytes

• 0 gigabytes

4. A gardener is planting flowers in two different sections of a garden. Section A has a linear growth rate of 3 flowers per week, while Section B has a growth rate of 5 flowers per week. If Section A starts with 10 flowers and Section B starts with 5, write the equations for the number of flowers in each section after t weeks. When will they have the same number of flowers?

• 4 weeks

• 2.5 weeks

• 1 week

• 3 weeks

5. A gym charges a monthly membership fee of $40 plus $2 for each class attended. Write the equation for the total cost (C) based on the number of classes (c) attended. If a member attends 10 classes, what is the total cost?

• $60

• $100

• $80

• $50

6. A delivery service charges a base fee of $15 plus $0.50 per mile. Write the linear equation for the total cost (C) based on the distance (d) in miles. What does the y-intercept represent in this scenario?

• C = 0.50d; y-intercept represents the delivery fee per mile.

• C = 15 + 0.25d; y-intercept represents the discount on the base fee.

• C = 15 + 0.50d; y-intercept represents the base fee of $15.

• C = 15d + 0.50; y-intercept represents the total cost at 0 miles.

7. Two friends are comparing their weekly allowances. Alex receives $10 per week, while Jamie receives $15 per week. Write the equations for their total allowances after w weeks. How much more does Jamie have than Alex after 6 weeks?

• 25 dollars

• 15 dollars

• 30 dollars

• 20 dollars

8. A bookstore sells novels for $12 each and textbooks for $25 each. Write the equations for the total cost (C) based on the number of novels (n) and textbooks (t) purchased. If a customer buys 3 novels and 2 textbooks, what is the total cost?

• 100

• 86

• 50

• 75

9. A local bakery sells cupcakes for $3 each and cookies for $2 each. Write the equations for the total cost (C) based on the number of cupcakes (c) and cookies (k) bought. If a customer buys 4 cupcakes and 5 cookies, how much do they spend?

• $22

• $18

• $25

• $15

10. A school is planning a field trip. The cost per student is $25, and there is a flat fee of $200 for the bus. Write the equation for the total cost (C) based on the number of students (s). What is the slope, and what does it represent in this context?

• C = 25s + 100; Slope = 25, representing the cost of the bus.

• C = 200s + 25; Slope = 200, representing the total cost per student.

• C = 25s; Slope = 200, representing the total bus fee.

• C = 25s + 200; Slope = 25, representing the cost per additional student.