Understanding Linear Relationships

The video tutorial explains the concept of linear relationships, distinguishing them from proportional relationships. It introduces the slope-intercept form of a linear equation, y = mx + b, where m is the slope and b is the y-intercept. Through examples, such as cable company pricing and computer purchase with internet fees, the tutorial demonstrates how to identify and calculate the slope and y-intercept, and how to represent these relationships graphically.

What distinguishes a linear relationship from a proportional relationship?

• A proportional relationship can have any y-intercept.

• A proportional relationship has a variable slope.

• A linear relationship can have a y-intercept that is not zero.

• A linear relationship always passes through the origin.

How do you calculate the slope of a line?

• By adding the rise and the run.

• By dividing the vertical change by the horizontal change.

• By multiplying the rise by the run.

• By dividing the horizontal change by the vertical change.

In the context of the video, what does the term 'rise over run' refer to?

• The increase in y-intercept

• The slope of the line

• The decrease in x-intercept

• The total cost

What does the 'M' represent in the equation y = MX + B?

• The y-intercept

• The slope

• The x-intercept

• The constant term

In the equation y = 70x + 100, what does the number 100 represent?

• The monthly fee

• The slope

• The y-intercept

• The total cost

For returning customers, what is the equation representing their monthly cost?

• y = 70x

• y = 100x + 70

• y = 100x

• y = 70x + 100

What is the initial cost when buying a new computer and paying for internet?

• $550

• $500

• $100

• $50

How much do you pay per month for internet after buying a new computer?

• $100

• $500

• $50

• $550

What is the y-intercept in the equation y = 50x + 500?

• 550

• 500

• 50

• 0

What pattern does the graph of a linear relationship create?

• A circle

• A zigzag

• A straight line

• A curve