Slope and Line Equations: Real-World Challenges for 7th Graders

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?

• 2

• 3/8

• 5/3

• 8/3

2. Using the slope from the previous problem, write the slope-intercept equation of the line that passes through point A (2, 3).

• y = mx + (3 - 2m)

• y = 3x + 2

• y = mx + 3

• y = 2x + 1

3. A bike path runs from point C (1, 2) to point D (4, 8). Calculate the slope of the bike path and explain what this slope represents in real-world terms.

• The slope of the bike path is 0.5.

• The slope of the bike path is 3.

• The slope of the bike path is 1.

• The slope of the bike path is 2.

4. If the slope of the bike path from point C to point D is used to write the equation of the line, what is the slope-intercept form of that equation?

• y = mx + b

• y = mx^2 + c

• y = b + mx

• y = m + b

5. A student measures the height of a plant at two points in time: at day 1 (0, 1) and day 5 (4, 5). What is the slope of the plant's growth?

• 2

• 0.5

• 3

• 1

6. Write the slope-intercept equation for the plant's growth based on the points measured.

• y = ax + c

• y = m + b

• y = mx^2 + b

• y = mx + b

7. A train travels from station X (3, 4) to station Y (7, 10). Determine the slope of the line representing the train's journey.

• 0.75

• 2.0

• 1.5

• 3.5

8. Using the slope from the train's journey, write the slope-intercept equation for the line that represents the train's path.

• y = mx + b

• y = m + bx

• y = b + mx

• y = mx^2 + c

9. A runner's distance over time is recorded at two points: (2, 5) and (6, 15). What is the slope of the runner's distance?

• 3.0

• 1.5

• 4.0

• 2.5

10. Based on the runner's distance, write the slope-intercept equation that models the runner's performance over time.

• y = (d/t)x

• y = d - t

• y = t/d

• y = d + t