Exploring Constant Rate of Change in Linear Functions

The video tutorial introduces the concept of linear relationships, explaining that they are characterized by a constant rate of change and a straight-line graph. The instructor provides examples to determine if a relationship is linear by analyzing changes in variables. The tutorial includes calculations of the constant rate of change using the change in y over the change in x. Students are encouraged to practice with additional examples, including graph analysis, to reinforce their understanding of linear relationships.

Why are graphs particularly useful in understanding relationships?

• They are required for all mathematical problems.

• They help in visualizing relationships between variables.

• They are easier to draw than tables.

• They make data look pretty.

What is a linear relationship?

• A relationship that forms a curved line on a graph.

• A relationship that forms a straight line on a graph.

• A relationship that has no pattern.

• A relationship that changes randomly.

How can you determine if a relationship is linear from a table of values?

• By checking if the values are all positive.

• By checking if the values are all negative.

• By checking if there is a constant rate of change.

• By checking if the values are all the same.

In the first example, what was the constant rate of change for the y-values?

• -10

• -30

• 3

• 10

What does the delta symbol (Δ) represent in the context of rate of change?

• The sum of values

• The division of values

• The product of values

• The difference between values

How do you calculate the constant rate of change?

• Change in y over change in x

• Sum of x and y

• Product of x and y

• Change in x over change in y

In the second example, what was the constant rate of change for the x-values?

• 30

• 8

• 1

• 10

What is the constant rate of change in the second example?

• 10

• 30

• 8

• 1

What variable is considered independent in the second example?

• Charge

• Rate

• Change

• Hours

How can you tell if a graph is linear?

• If the line is zigzag

• If the line is dotted

• If the line is straight

• If the line is curved