Slope Interpretations: Real-World Linear Challenges

1. A car travels from point A (2, 3) to point B (6, 7). What is the slope of the line connecting these two points, and what does it represent in the context of the car's journey?

• 0.5

• 2

• 1

• 3

3. A store sells notebooks for $2 each and pens for $1 each. If the total cost for 5 notebooks and 3 pens is represented by the points (5, 10) and (3, 5), find the slope and interpret its meaning in this context.

• 2.5

• 3.0

• 4.0

• 1.5

4. The temperature in a city increases from 20°C to 30°C over a period of 4 hours. If this change is represented by the points (0, 20) and (4, 30), calculate the slope and explain what it indicates about the temperature change per hour.

• 10°C per hour

• 5°C per hour

• 2.5°C per hour

• 1°C per hour

5. A bike rental company charges a flat fee of $10 plus $2 for each hour rented. If the total cost for 3 hours is represented by the points (3, 16) and (0, 10), find the slope and write the equation in slope-intercept form.

• y = 3x + 10

• y = 2x + 12

• y = 2x + 8

• y = 2x + 10

6. A student scores 70 on their first test and 90 on their second test. If these scores are represented by the points (1, 70) and (2, 90), determine the slope and explain what it means in terms of the student's improvement.

• 20

• 15

• 25

• 30

7. A gardener plants flowers in a straight line. If the number of flowers planted increases from 5 to 15 over a distance of 10 meters, find the slope and write the equation of the line in slope-intercept form.

• y = 2x + 1

• y = x - 5

• y = x + 5

• y = 3x + 2

8. A train travels from station A (0, 50) to station B (5, 80). Calculate the slope of the line and interpret what this slope means in terms of the train's speed.

• 6

• 4

• 10

• 8

9. A company’s profit increases from $2000 to $5000 over 3 years. If this change is represented by the points (0, 2000) and (3, 5000), find the slope and explain its significance in the context of the company's growth.

• The slope is 200.

• The slope is 1500.

• The slope is 1000.

• The slope is 500.

10. A student’s height increases from 140 cm to 160 cm over 2 years. If these heights are represented by the points (0, 140) and (2, 160), calculate the slope and describe what it indicates about the student's growth rate per year.

• 10 cm per year

• 5 cm per year

• 20 cm per year

• 15 cm per year