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The graph shows the linear relationship between the height of a plant (in centimeters) and the time (in weeks) that the plant has been growing.

Which statements are correct? Check all that apply.

The rate of change is 4.
The rate of change is 1.
The rate of change is 4/1.
The plant grows 4 cm in 1 week.
The plant grows 1 cm in 4 weeks.

Axes:

x-axis: Time (weeks)
y-axis: Height (cm)

Data Points:

The graph features several points showing height at different weeks, suggesting a steady increase:
At Week 1, the height is around 8 cm.
At Week 2, the height increases to approximately 12 cm.
At Week 3, the height is about 16 cm.
At Week 4, the height reaches 20 cm.

1 answer

To determine which statements are correct, let's first analyze the provided data points and calculate the rate of change. The data points indicate a linear increase in height over time:

  • At Week 1: 8 cm
  • At Week 2: 12 cm
  • At Week 3: 16 cm
  • At Week 4: 20 cm

To find the rate of change of height with respect to time, we observe the increase in height over the increase in time:

  1. From Week 1 to Week 2:

    • Increase in height: \(12 cm - 8 cm = 4 cm\)
    • Increase in time: \(2 weeks - 1 week = 1 week\)
    • Rate of change: \(\frac{4 cm}{1 week} = 4 , \text{cm/week}\)

  2. From Week 2 to Week 3:

    • Increase in height: \(16 cm - 12 cm = 4 cm\)
    • Increase in time: \(3 weeks - 2 weeks = 1 week\)
    • Rate of change: \(\frac{4 cm}{1 week} = 4 , \text{cm/week}\)

  3. From Week 3 to Week 4:

    • Increase in height: \(20 cm - 16 cm = 4 cm\)
    • Increase in time: \(4 weeks - 3 weeks = 1 week\)
    • Rate of change: \(\frac{4 cm}{1 week} = 4 , \text{cm/week}\)

Throughout all the comparisons, the rate of change remains consistent at 4 cm per week.

Now, let's evaluate the provided statements:

  1. The rate of change is 4. (Correct)
  2. The rate of change is 1. (Incorrect)
  3. The rate of change is 4/1. (Correct, since 4/1 equals 4)
  4. The plant grows 4 cm in 1 week. (Correct)
  5. The plant grows 1 cm in 4 weeks. (Incorrect, as the plant grows 4 cm in 1 week, not 1 cm in 4 weeks)

Summary of Correct Statements:

  • The rate of change is 4.
  • The rate of change is 4/1.
  • The plant grows 4 cm in 1 week.