Slope Interpretations: A Linear Equations Challenge

1. A car travels from point A (2, 3) to point B (6, 7). What is the slope of the line representing the car's path?

• 2

• 3

• 1

• 0.5

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

• y = 2x - 1

• y = 2x + 2

• y = x + 2

• y = 2x + 4

3. A bike rental shop charges a flat fee of $10 plus $2 for each hour rented. Write a linear equation to represent the total cost (C) in terms of hours rented (h). What is the slope in this context?

• C = 10 + 2h; slope = 2

• C = 5 + 2h; slope = 2

• C = 10 + 3h; slope = 3

• C = 10 + h; slope = 1

4. A student scores 80 on their first test and 90 on their second test. If the scores are plotted on a graph, what is the slope of the line connecting these two points?

• 20

• 10

• 5

• 15

5. A gardener plants flowers in a straight line. If the first flower is planted at (0, 1) and the second at (4, 5), what is the slope of the line? What does this slope represent in the context of the garden?

• 2

• 1

• 0.5

• -1

6. The temperature in a city increases from 30°F at 8 AM to 50°F at 12 PM. Calculate the slope of the temperature change and interpret it in context.

• 2°F/hour

• 10°F/hour

• 5°F/hour

• 15°F/hour

7. A train travels from station A (3, 2) to station B (7, 6). Find the slope of the line representing the train's journey and write the equation of the line in slope-intercept form.

• y = x - 1

• y = 2x + 1

• y = -x + 5

• y = 3x - 2

8. A store sells notebooks for $3 each. If the total cost (C) is represented as a function of the number of notebooks (n), what is the slope of this linear equation?

• 2

• 4

• 3

• 5

9. A line passes through the points (2, 5) and (4, 9). Calculate the slope and identify the y-intercept of the line. Write the equation in slope-intercept form.

• y = 2x + 1

• y = 4x - 1

• y = x + 5

• y = 3x + 2

10. A runner completes a 5K race, finishing at (10, 15) minutes. If the runner started at (0, 0) minutes, what is the slope of the line representing their pace? What does this slope indicate about their speed?

• 3 minutes per kilometer

• 1.5 minutes per kilometer

• 2 minutes per kilometer

• 1 minute per kilometer