Understanding Linear Relationships and Costs

The video tutorial explains proportional relationships, highlighting their constant ratio and graph characteristics. It uses a theme park example to illustrate the concept, showing how to calculate costs and plot points on a graph. The tutorial further explores the slope and rate of change, explaining why the example is not a proportional relationship due to varying ratios.

What is a key characteristic of a proportional relationship?

• The graph is a curve.

• The ratio between two quantities is constant.

• The relationship has a variable rate of change.

• The graph does not pass through the origin.

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

• The total cost of visiting the park with x tickets.

• The cost of a single ride.

• The distance to the park.

• The number of rides available.

If you buy 4 tickets, what is the total cost according to the equation y = 2x + 20?

• $36

• $28

• $24

• $32

What pattern is observed in the changes of total cost as more tickets are purchased?

• The cost increases by $4 each time.

• The cost decreases by $2 each time.

• The cost doubles each time.

• The cost remains the same.

What does the slope of the line represent in the context of the theme park example?

• The number of tickets purchased.

• The rate of change in total cost per ticket.

• The distance between rides.

• The total cost of entry.

How is the slope calculated from the table of values?

• By multiplying the change in y by the change in x.

• By dividing the change in x by the change in y.

• By dividing the change in y by the change in x.

• By adding the changes in x and y.

What does the term 'rise over run' refer to in the context of graphing?

• The distance between points.

• The slope of the line.

• The total cost of tickets.

• The number of tickets purchased.

Why is the relationship in the theme park example not proportional?

• The graph is a straight line.

• The ratios of y over x are not constant.

• The equation has a constant term.

• The slope is not equal to 1.

What is the result of dividing 32 by 6 in the context of the theme park example?

• A repeating decimal.

• A constant ratio.

• A whole number.

• A non-repeating decimal.

What does the equation y = 2x + 20 fail to do that a proportional relationship would?

• Have a constant slope.

• Pass through the origin.

• Represent a straight line.

• Include a variable term.