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

Question

The table shows time in hours as 0, 1, 3, and distance in miles as 3, 4.25, 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.

Answer 1

To analyze the statements, we will first examine the data given in the table:

| Time (hours) | Distance (miles) | |--------------|------------------| | 0 | 3 | | 1 | 4.25 | | 3 | 6.75 |

Statement Analysis

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

   • From the table, when time = 0 hours, Amanda's distance from school is 3 miles.
   • True or False: False

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

   • Calculate the distance increase from time 0 to time 1:
     • From 3 miles (at time 0) to 4.25 miles (at time 1):
     • Increase = 4.25 - 3 = 1.25 miles.
   • Calculate the distance increase from time 1 to time 3:
     • From 4.25 miles (at time 1) to 6.75 miles (at time 3):
     • Increase = 6.75 - 4.25 = 2.5 miles over 2 hours, which is 1.25 miles per hour.
   • Since Amanda increases her distance by 1.25 miles for each hour consistently based on this data:
   • True or False: True

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

   • Since her distance increases by 1.25 miles per hour, we can calculate the distance after 4 hours:
     • Distance after 0 hours: 3 miles
     • After 1 hour: 3 + 1.25 = 4.25 miles
     • After 2 hours: 4.25 + 1.25 = 5.5 miles
     • After 3 hours: 5.5 + 1.25 = 6.75 miles
     • After 4 hours: 6.75 + 1.25 = 8 miles.
   • Thus, after 4 hours, Amanda's distance from school is 8 miles, not 9.75 miles.
   • True or False: False

Summary of Truth Values:

• Amanda's initial distance from her school is 1.25 miles: False
• Amanda's distance increases by 1.25 miles each hour: True
• Amanda's distance from school after 4 hours is 9.75 miles: False