Understanding Slope and y-Intercept in Real-Life Scenarios

1. A car travels from point A (2, 3) to point B (6, 7). What is the slope of the line representing the car's path, and what does this slope indicate about the car's speed?

• The slope is 1, indicating a constant speed.

• The slope is 2, indicating a variable speed.

• The slope is 0, indicating the car is stationary.

• The slope is -1, indicating the car is moving backwards.

2. A gardener plants flowers in a straight line. The first flower is at the point (1, 2) and the second flower is at (4, 5). What is the slope of the line between these two points, and what does it tell you about the growth rate of the flowers?

• The slope is -1.

• The slope is 1.

• The slope is 0.

• The slope is 2.

3. A bike rental service charges a flat fee of $5 plus $2 for every hour rented. If the cost is represented by the equation y = 2x + 5, identify the y-intercept and explain its significance in this context.

• The y-intercept is 7, which includes a discount for the first hour of rental.

• The y-intercept is 5, representing the flat fee charged for renting a bike.

• The y-intercept is 0, indicating there is no initial fee for renting a bike.

• The y-intercept is 2, representing the hourly charge for renting a bike.

4. A student scores 70 on their first test and 90 on their second test. If we plot these points (1, 70) and (2, 90), what is the slope of the line connecting these points, and what does it represent about the student's improvement?

• 30

• 10

• 50

• 20

5. A train travels from station X (0, 0) to station Y (5, 10). Calculate the slope of the line and interpret what this slope means in terms of the train's speed.

• The slope of the line is 0.5.

• The slope of the line is 2.

• The slope of the line is 1.

• The slope of the line is 3.

6. A restaurant's revenue can be modeled by the equation y = 3x + 20, where x is the number of customers. Identify the y-intercept and explain what it represents in the context of the restaurant's business.

• The y-intercept is 3.

• The y-intercept is 0.

• The y-intercept is 10.

• The y-intercept is 20.

7. A runner completes a 5 km race in 25 minutes. If we plot the distance (in km) against time (in minutes) using the points (0, 0) and (5, 25), what is the slope, and what does it indicate about the runner's pace?

• The slope is 0.1 km/min, indicating the runner's pace is 10 minutes per kilometer.

• The slope is 0.2 km/min, indicating the runner's pace is 5 minutes per kilometer.

• The slope is 1 km/min, indicating the runner's pace is 1 minute per kilometer.

• The slope is 0.4 km/min, indicating the runner's pace is 2.5 minutes per kilometer.

8. A company’s profit can be modeled by the equation y = 4x + 50, where x is the number of products sold. What is the y-intercept, and what does it signify for the company?

• 60

• 40

• 70

• 50

9. A student’s height is measured at ages 10 and 12, resulting in the points (10, 140) and (12, 150). Calculate the slope and interpret what this means about the student's growth over those two years.

• The slope is 5, indicating the student grew 5 cm per year.

• The slope is 0, indicating the student did not grow at all.

• The slope is 2.5, indicating the student grew 2.5 cm per year.

• The slope is 10, indicating the student grew 10 cm per year.

10. A city’s population grows from 100,000 to 120,000 over 5 years. If we represent this with the points (0, 100000) and (5, 120000), what is the slope of the line, and what does it indicate about the city's growth rate?

• The slope of the line is 4000, indicating a growth rate of 4000 people per year.

• The slope of the line is 2000, indicating a growth rate of 2000 people per year.

• The slope of the line is 3000, indicating a growth rate of 3000 people per year.

• The slope of the line is 5000, indicating a growth rate of 5000 people per year.