Understanding Linear Relationships and Functions

The video tutorial explains proportional relationships, highlighting their constant ratio and graph characteristics. It uses a theme park cost example to illustrate a non-proportional relationship, showing how to calculate costs, plot points, and understand slope and rate of change. The tutorial concludes by explaining why the example is not proportional, emphasizing the importance of consistent ratios in proportional relationships.

What is a key characteristic of a proportional relationship?

• The graph is a curve.

• The relationship has a variable rate of change.

• The ratio between two quantities is constant.

• The graph does not pass through the origin.

Which of the following is true for a proportional relationship?

• The graph has a variable slope.

• The graph is a straight line not through the origin.

• The graph is a straight line through the origin.

• The graph is a curve.

In the Mountain World theme park example, what does the number 20 represent in the equation y = 2x + 20?

• The cost of one ticket.

• The entrance fee to the park.

• The cost of food and games.

• The total cost for two tickets.

How much does the total cost increase when two additional tickets are purchased?

• $2

• $4

• $10

• $8

What is the slope of the line represented by the equation y = 2x + 20?

• 1

• 2

• 4

• 20

When plotting the points for the equation y = 2x + 20, what is the y-value when x equals 4?

• 28

• 32

• 24

• 20

What is the value of y when x equals 0 in the equation y = 2x + 20?

• 22

• 20

• 0

• 2

What does the slope of a line represent in a graph?

• The rate of change between x and y.

• The x-intercept of the line.

• The y-intercept of the line.

• The total cost of tickets.

Why is the relationship described by y = 2x + 20 not proportional?

• The graph is not a straight line.

• The x-values are not consistent.

• The slope is not constant.

• The y-intercept is not zero.

What is the result of dividing 32 by 6 in the context of the table of values?

• 5.33

• 32

• 16/3

• 6