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Does the table represent a linear function?

In each of the tabs shown below, you will find a table filled with data. Above the table is a statement describing what the data represents. In each example, determine whether the rate is constant and represents a linear function based on the rate of change.

Aquarium

Student Hiking

Printer Assembly

Car Mileage

Savings Account

A 160 liter aquarium must be drained.

Point Water in Tank (liters) Time (min) Change in Water Change in Time
1 160 0 --- ---
2 145 1 -15 1
3 115 3 -30 2
4 70 6 -45 3
5 40 8 -30 2
6 10 10 -30 2

This table represents a linear function because the slope is -15, which is consistent from point to point.

A student is hiking 25 miles.

Point Distance Time Change in Distance Change in Time
1 0 0 --- ---
2 5 20 5 10
3 10 30 5 20
4 15 40 5 10
5 20 60 5 20
6 25 75 5 15

This is not a linear function because the slope is not the same for all points on the table.

This is the time it takes to assemble a printer. Each printer has 16 parts.

Point Total Parts Time (hours) Change in Items Change in Time
1 0 0 --- ---
2 16 2 16 2
3 32 4 16 2
4 48 6 16 2
5 64 8 16 2

This table represents a linear function because the slope is 8, which is consistent from point to point.

This is the mileage in a car in miles per gallon.

Point Miles Traveled Fuel Used (gallons) Change in Miles Change in Gallons
1 0 0 --- ---
2 45 1.5 45 1.5
3 60 2 15 0.5
4 105 3.5 45 1.5
5 120 4 15 0.5

This table represents a linear function because the slope is 30, which is consistent from point to point.

This is the data for a savings account college fund.

Point Bank Balance ($) Total Time (Month) Change in Bank Balance Change in Time
1 500 0 --- ---
2 620 6 120 6
3 710 9 90 3
4 830 15 120 6
5 910 17 80 2
6 1050 24 140 7

This is not a linear function because the slope changes from point to point and is not consistent.