Real-Life Slope Challenges: Graphs and Problem Solving

1. A car travels on a straight road and the graph shows its distance from a starting point over time. If the line on the graph rises 3 units for every 2 units it moves to the right, what is the slope of the line?

• 3/2

• 4/3

• 2/3

• 1/2

2. A mountain trail is represented by a graph where the vertical axis shows elevation in meters and the horizontal axis shows distance in kilometers. If the trail rises from 200 meters to 600 meters over 4 kilometers, what is the slope of the trail?

• 50 meters per kilometer

• 200 meters per kilometer

• 150 meters per kilometer

• 100 meters per kilometer

3. A bike rental service charges a flat fee of $10 plus $2 for every hour rented. If you graph the total cost against the number of hours, what is the slope of the line?

• 5

• 0

• 10

• 2

4. A student plots the number of hours studied against the score received on a test. If the graph shows a line that rises 5 points for every 1 hour studied, what does the slope represent in this context?

• The slope represents the maximum score achievable.

• The slope shows the average score of all students.

• The slope indicates the total hours studied.

• The slope represents the increase in test score per hour studied.

5. A company’s profit over time is graphed, showing a steady increase. If the profit increases from $1000 to $4000 over 3 years, what is the slope of the profit line?

• 2000

• 1500

• 500

• 1000

6. A gardener measures the height of a plant over weeks. If the height increases from 10 cm to 30 cm over 4 weeks, what is the slope of the height graph?

• 10 cm/week

• 5 cm/week

• 2 cm/week

• 15 cm/week

7. A train travels from one city to another, and the graph shows its speed over time. If the speed increases from 20 km/h to 80 km/h over 2 hours, what is the slope of the speed line?

• 30 km/h

• 60 km/h

• 50 km/h

• 40 km/h

8. A school tracks the number of books read by students over a month. If the graph shows that for every 5 books read, the number of students increases by 2, what is the slope of the line?

• 0.5

• 1.0

• 0.4

• 0.2

9. A water tank is filled at a constant rate. If the graph shows the water level rising from 50 liters to 150 liters in 5 minutes, what is the slope of the water level graph?

• 10 liters per minute

• 15 liters per minute

• 30 liters per minute

• 20 liters per minute

10. A runner's distance over time is graphed, showing a steady pace. If the runner covers 10 kilometers in 50 minutes, what is the slope of the distance-time graph?

• 0.1 km/min

• 0.2 km/min

• 0.5 km/min

• 1 km/min