Calculating and Interpreting Slope in Real-Life Scenarios

A line on a graph passes through the points (2, 3) and (5, 9). What is the slope of the line?

• 3

• 4

• 1

• 2

If a car travels 150 miles in 3 hours, what is the slope of the distance-time graph? Interpret what this slope means in the context of the car's speed.

• 100 miles per hour

• 30 miles per hour

• 50 miles per hour

• 75 miles per hour

A line representing the temperature over time shows a rise from (1, 20) to (4, 35). Calculate the slope and explain what it indicates about the temperature change.

• The slope is 10, indicating a temperature decrease of 10 degrees per time unit.

• The slope is 5, indicating a temperature increase of 5 degrees per time unit.

• The slope is 5, indicating no change in temperature over time.

• The slope is 3, indicating a temperature increase of 3 degrees per time unit.

A bike rental company charges a flat fee of $10 plus $2 per hour. If you graph the total cost against hours rented, what is the slope of the line? What does this slope represent?

• 10

• 5

• 2

• $2 per hour

A student scores 80 on their first test and 90 on their second test, with the tests spaced 2 weeks apart. Calculate the slope of the score graph and interpret its meaning in terms of improvement over time.

• 15

• -5

• 10

• 5

A plant grows from 10 cm to 25 cm over 5 weeks. What is the slope of the growth graph? What does this slope tell you about the plant's growth rate?

• 2 cm/week

• 3 cm/week

• 5 cm/week

• 1 cm/week

A runner completes a 5K race in 25 minutes. If you graph the distance against time, what is the slope of the line? What does this slope indicate about the runner's pace?

• 3.33 meters/second

• 5.0 meters/second

• 2.5 meters/second

• 4.0 meters/second

A factory produces 200 units in the first hour and 500 units in the fourth hour. Calculate the slope of the production graph and interpret what this means for the factory's output over time.

• 150 units per hour

• 200 units per hour

• 250 units per hour

• 100 units per hour

A student reads 30 pages in the first hour and 60 pages in the second hour. What is the slope of the pages read graph? What does this slope indicate about the student's reading speed?

• 30 pages per hour

• 60 pages per hour

• 45 pages per hour

• 90 pages per hour

A water tank is filled at a rate of 4 liters per minute. If you graph the volume of water against time, what is the slope of the line? Interpret this slope in the context of the tank's filling process.

• 4 liters per minute

• 10 liters per minute

• 2 liters per minute

• 1 liter per minute