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The relationship between Amanda's distance from school and time since she left school is linear, as shown in the table below.

Time (hours)
Distance (miles)

3
1
4.25
3
6.75
Based on the table, determine whether each statement is true or false.
True
False
Amanda's initial distance from her school is 1.25 miles.
Amanda's distance increases by 1.25 miles each hour.
Amanda's distance from school after 4 hours is 9.75 miles.

1 answer

To analyze the statements given the data, we first need to look at the relationship between time and distance according to the points in the table. The provided information seems to lack some clarity, but let's assume we interpret it as follows using the points provided:

  • At 3 hours, the distance is 1 mile.
  • At 4.25 hours, the distance is 3 miles.
  • At 6.75 hours, the distance is not explicitly stated, but we can infer it as necessary.

From the information given, we need to determine:

  1. The initial distance from her school.
  2. The rate of distance increase per hour.
  3. The distance from school after 4 hours.

Statement Analysis

  1. "Amanda's initial distance from her school is 1.25 miles."

    • False. The distance at 3 hours is 1 mile. To find the initial distance (at 0 hours), we would need to establish the linear equation and extrapolate backwards.

  2. "Amanda's distance increases by 1.25 miles each hour."

    • False. Between the two known data points:
      • From 1 mile at 3 hours to 3 miles at 4.25 hours, which is an increase of 2 miles over 1.25 hours, resulting in an average rate of: \[ \text{Rate} = \frac{3 - 1}{4.25 - 3} = \frac{2}{1.25} = 1.6 \text{ miles per hour.} \] This linear increase per hour is not 1.25 miles.

  3. "Amanda's distance from school after 4 hours is 9.75 miles."

    • False. Based on the distance noted at 4.25 hours (3 miles), we need to find out what her distance would be at 4 hours. If we assume the linear relationship, we can calculate it as follows:
      • From the previous calculation, we understand she travels 1.6 miles per hour. Therefore, we can determine distance by taking: \[ \text{Distance at 4 hours} = 1 + (\text{rate} \times \text{time}) = 1 + (1.6 \times 1) \text{ (1 hour from 3 to 4)} = 1 + 1.6 = 2.6 \text{ miles.} \] This indicates she wouldn't be at 9.75 miles.

Based on the derived calculations, all statements are false.