Exploring Slope and Y-Intercept in Real-Life Scenarios

1. A car rental company charges a flat fee of $50 plus $0.20 per mile driven. Write the 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 = 50 + 0.20m; Slope = 0.20 (cost per mile)

• C = 50 + 0.20m; Slope = 1.00 (cost per mile)

• C = 50 + 0.10m; Slope = 0.10 (cost per mile)

• C = 50 + 0.50m; Slope = 0.50 (cost per mile)

2. The equation of a line is given as y = 3x + 5. Identify the slope and the y-intercept of this line. What do these values represent in a real-world scenario?

• Slope: 5, Y-intercept: 3

• Slope: 3, Y-intercept: 0

• Slope: 3, Y-intercept: 5

• Slope: 0, Y-intercept: 5

3. A gardener is planting flowers in a straight line. The equation of the line representing the height of the flowers over time is y = 2x + 4. What is the slope, and what does it indicate about the growth of the flowers?

• The slope is 2, indicating the flowers grow 2 units in height for every 2 units of time.

• The slope is 2, indicating the flowers grow 2 units in height for each unit of time.

• The slope is 1, indicating the flowers grow 1 unit in height for each unit of time.

• The slope is 4, indicating the flowers grow 4 units in height for each unit of time.

4. A school is planning a fundraiser. The total amount raised can be modeled by the equation y = 150x + 300, where x is the number of weeks. What is the y-intercept, and what does it signify?

• 150

• 3000

• 300

• 450

5. A bike rental service charges a base fee of $15 and $1.50 for each hour rented. If you graph the total cost against the number of hours, what is the y-intercept and what does it represent?

• The y-intercept is 15, representing the base fee of the bike rental service.

• The y-intercept is 30, representing a discount for renting multiple hours.

• The y-intercept is 0, representing no cost for renting a bike.

• The y-intercept is 1.50, representing the cost per hour.

6. The line representing the temperature in a city over time is given by the equation y = -2x + 30. Identify the slope and explain what it means in terms of temperature change.

• The slope is 2.

• The slope is -2.

• The slope is -30.

• The slope is 0.5.

7. A delivery service charges a fee of $10 plus $0.50 per mile. Write the equation for the total cost and identify the slope. What does the slope represent in this situation?

• C = 10 + 0.75m; slope = 0.75, representing the cost per mile.

• C = 5 + 0.25m; slope = 0.25, representing the delivery fee.

• C = 10 + 1.00m; slope = 1.00, representing the total cost.

• C = 10 + 0.50m; slope = 0.50, representing the cost per mile.

8. A local gym has a membership fee of $25 and charges $10 per class attended. If you graph the total cost against the number of classes, what is the y-intercept and what does it indicate?

• The y-intercept is 25, indicating the initial membership fee.

• The y-intercept is 10, indicating the cost per class.

• The y-intercept is 25, indicating the cost of each class.

• The y-intercept is 0, indicating no initial cost.

9. The equation of a line representing the distance traveled by a runner over time is y = 4x + 10. What is the slope, and how does it relate to the runner's speed?

• The slope is 10, indicating the runner's speed is 10 units per time unit.

• The slope is 2, indicating the runner's speed is 2 units per time unit.

• The slope is 4, indicating the runner's speed is 8 units per time unit.

• The slope is 4, indicating the runner's speed is 4 units per time unit.

10. A phone company offers a plan that costs $30 per month plus $0.10 per text message. Write the equation for the total monthly cost and identify the y-intercept. What does it represent in this context?

• C = 20 + 0.10x; y-intercept = 20, representing a discount on the base cost.

• C = 30 + 0.05x; y-intercept = 0, representing the cost per text message.

• C = 30 + 0.20x; y-intercept = 30, representing the total cost for one text message.

• C = 30 + 0.10x; y-intercept = 30, representing the base cost of the plan.