Calculating and Interpreting Slope in Real-Life Scenarios

1. A car travels from point A (2, 3) to point B (6, 11). What is the slope of the line representing the car's path?

• 3

• 2

• 4

• 1

2. If the slope of a line is 2 and it passes through the point (1, 4), what is the equation of the line in slope-intercept form?

• y = 2x + 4

• y = 2x + 2

• y = x + 4

• y = 2x - 2

3. A bike rental company charges a flat fee of $5 plus $2 for each hour of rental. What is the slope of the cost function in relation to time?

• 2

• $5

• 1

• 3

4. A student scores 70 points on their first test and 90 points on their second test. If the tests were taken 2 weeks apart, what is the slope of the student's score over time?

• 15 points per week

• 20 points per week

• 10 points per week

• 5 points per week

5. A gardener plants flowers in a straight line. If the first flower is planted at (0, 0) and the second at (4, 8), what is the slope of the line formed by the flowers?

• 2

• 3

• 1

• 4

6. A train travels from station X (1, 2) to station Y (5, 10). What does the slope of the line tell you about the train's speed?

• The slope indicates the train is accelerating rapidly.

• The slope shows the train is moving backwards.

• The slope of the line indicates the train's speed is consistent, moving 2 units vertically for every 1 unit horizontally.

• The slope represents the distance traveled by the train.

7. A mountain trail rises from a base camp at (0, 0) to a peak at (3, 9). Calculate the slope of the trail and interpret what this means for hikers.

• The slope of the trail is 3.

• The slope of the trail is 4.

• The slope of the trail is 1.

• The slope of the trail is 2.

8. A company’s profit increases from $2000 to $5000 over 3 years. What is the slope of the profit line, and what does it indicate about the company’s growth?

• The slope of the profit line is 500, indicating the company’s profit increases by $500 per year.

• The slope of the profit line is 1000, indicating the company’s profit increases by $1000 per year.

• The slope of the profit line is 1500, indicating the company’s profit increases by $1500 per year.

• The slope of the profit line is 2000, indicating the company’s profit increases by $2000 per year.

9. A swimmer's speed increases from 1.5 m/s to 3.5 m/s over a distance of 100 meters. Calculate the slope of the speed graph and explain its significance.

• 0.05 s^-1

• 0.02 s^-1

• 0.01 s^-1

• 0.03 s^-1

10. A city’s population grows from 50,000 to 70,000 over 5 years. What is the slope of the population growth, and what does it imply about the city's development?

• The slope of the population growth is 4,000.

• The slope of the population growth is 10,000.

• The slope of the population growth is 2,000.

• The slope of the population growth is 5,000.