Exploring Linear Relationships

The video tutorial reviews linear relationships, explaining how they can be represented through equations, graphs, tables, and words. It discusses the characteristics of linear relationships, such as forming a straight line and having a constant rate of change. The tutorial also covers proportional relationships, highlighting the constant of proportionality and how it relates to linear equations. Through examples, the video demonstrates how to analyze equations for linearity and proportionality. Finally, it applies these concepts to a real-world scenario involving a gym membership, illustrating how to model and graph the relationship between visits and account balance.

Which of the following can represent a linear relationship?

• Only an equation

• Only a graph

• Only a table

• An equation, a graph, a table, or words

What is the constant rate of change in the equation y = x?

• 1

• 0

• x

• 2

How can you identify a proportional relationship in a linear equation?

• The equation passes through the origin and x is multiplied by a constant

• The table of values shows a constant difference

• The equation has a constant rate of change

• The graph is a straight line

In the equation y = -4x, what is the constant of proportionality?

• -4

• x

• y

• 4

Why is the equation y = 2x + 4 not considered proportional?

• The equation does not pass through the origin

• The rate of change is not constant

• It does not form a straight line

• x is not multiplied by a constant

What is the rate of change in the equation y = 2x + 4?

• 4

• 2

• 1

• 6

In the gym visit scenario, what is the independent variable?

• The amount of money in the account

• The initial deposit

• The deduction per visit

• The number of visits

How much money is deducted from Lucy's account per gym visit?

• $12

• $5

• $7

• $10

What is the initial amount of money in Lucy's account?

• $200

• $240

• $210

• $224

What is the equation representing the relationship between the number of gym visits and the account balance?

• y = 224 + 7x

• y = 224 - 7x

• y = 7x - 224

• y = 7x + 224