Understanding Linear Relations

The video explains linear relations, which occur when a quantity changes at a constant rate. It uses examples like a balloon rising at a constant rate and a bank account decreasing due to weekly spending. The video demonstrates how to represent these relations using tables and graphs, highlighting the importance of start values and rates. It also explains how to identify linear relations by checking if the first differences are constant.

What is a linear relation characterized by?

• A constant rate of change

• An exponential rate of change

• A fluctuating rate of change

• A variable rate of change

In the balloon example, what is the start value?

• 5 meters

• 8 meters

• 3 meters

• 2 meters per second

How is the rate of change represented in a table of values?

• As the difference between consecutive time values

• As the difference between consecutive height values

• As the sum of all height values

• As the sum of all time values

What shape does the graph of a linear relation form?

• A curved line

• A zigzag line

• A straight line

• A dotted line

Why is the graph of a linear relation a straight line?

• Because the time intervals are irregular

• Because the rate of change is variable

• Because the rate of change is constant

• Because the start value is zero

In the bank account example, what is the rate of change?

• Positive $20 per week

• Negative $20 per week

• Positive $200 per week

• Negative $200 per week

What does a negative rate indicate in a linear relation?

• An increase over time

• A decrease over time

• No change over time

• A fluctuating change over time

How is a decreasing linear relation graphically represented?

• As a line that slopes upwards

• As a line that slopes downwards

• As a horizontal line

• As a vertical line

Why might a dashed line be used in the graph of a decreasing linear relation?

• To indicate a positive rate

• To indicate discrete spending

• To indicate a variable rate

• To indicate continuous spending

What does the straight line in a graph of a linear relation signify?

• Constant first differences

• Increasing first differences

• Decreasing first differences

• Variable first differences