Calculating and Interpreting Slope in Real-Life Situations

1. A car travels from point A (2, 3) to point B (5, 11). What is the slope of the line connecting these two points?

• 5

• 3/8

• 2

• 8/3

2. If the slope of a line representing the cost of gas is 0.25, what does this slope mean in the context of gas prices?

• The cost of gas increases by $0.25 for every two units increase in the independent variable.

• The cost of gas increases by $0.25 for each unit increase in the independent variable.

• The cost of gas remains constant regardless of the independent variable.

• The cost of gas decreases by $0.25 for each unit increase in the independent variable.

3. A bike path rises from a point (1, 2) to (4, 8). Calculate the slope of the bike path and interpret what this means for the steepness of the path.

• The slope of the bike path is 0.5.

• The slope of the bike path is 1.

• The slope of the bike path is 2.

• The slope of the bike path is 3.

4. A student scores 70 points on their first test and 90 points on their second test. If the tests are spaced 3 weeks apart, what is the slope of the line representing their score over time?

• 5.00

• 8.00

• 10.00

• 6.67

5. A building is being constructed and rises from a height of 10 feet at point (0, 10) to 30 feet at point (5, 30). What is the slope of the building's height over this distance?

• 8

• 4

• 6

• 2

6. If a runner completes a 5 km race in 20 minutes and another in 25 minutes, what is the slope of the line representing their speed over time?

• -0.01

• -0.02

• 0.05

• 0.01

7. A farmer sells apples at a price of $2 per pound. If the price increases to $3 per pound after selling 100 pounds, what is the slope of the price per pound in relation to the quantity sold?

• 0.2

• 0.01

• 0.05

• 0.1

8. A train travels from station A (0, 0) to station B (10, 50). Calculate the slope and explain what this means in terms of the train's speed.

• The slope of the train's path is 0.5.

• The slope of the train's path is 10.

• The slope of the train's path is 2.

• The slope of the train's path is 5.

9. A student’s grades increase from 60 to 90 over 4 tests. What is the slope of the line representing their grades, and what does it indicate about their performance?

• 5

• 10

• 20

• 15

10. A mountain trail rises from a base elevation of 500 feet at point (0, 500) to an elevation of 1500 feet at point (4, 1500). What is the slope of the trail, and how does it reflect the difficulty of the hike?

• 1000 feet per mile

• 500 feet per mile

• 1500 feet per mile

• 250 feet per mile