Understanding Direct Variation in Aluminum Can Usage

The video tutorial explains the concept of direct variation, where the number of aluminum cans used varies directly with the number of people using them. It introduces the direct variation equation y = kx, where k is the variation constant. The tutorial demonstrates how to calculate k using given data and applies the equation to solve a real-world problem involving a city's population. Finally, it discusses the graph of the equation, highlighting the slope and intercept.

What does it mean when we say the number of aluminum cans varies directly with the number of people?

• The number of cans increases as the number of people decreases.

• The number of cans decreases as the number of people increases.

• The number of cans is constant regardless of the number of people.

• The number of cans increases proportionally with the number of people.

Which equation represents a direct variation relationship?

• y = k/x

• y = x^2 + k

• y = kx

• y = mx + b

How do you calculate the variation constant 'k' in a direct variation?

• Divide y by x

• Add y and x

• Multiply y by x

• Subtract x from y

If 500 people use 120,000 cans, what is the variation constant?

• 500

• 120,000

• 240

• 600

What is the equation that models the relationship between the number of cans and people?

• y = 240x

• y = 500x

• y = x/240

• y = 120,000x

How many cans are used in a city with a population of 130,000?

• 31,200,000

• 240,000

• 120,000

• 500,000

What does the slope of the line in the graph of y = 240x represent?

• The change in population

• The total number of cans used

• The number of people per can

• The number of cans used per person

In the context of the graph, what is the y-intercept of the equation y = 240x?

• 240

• 0

• 130,000

• 120,000

If the population increases by one, how many more cans are used according to the slope?

• 1

• 240

• 500

• 120,000

What is the primary concept illustrated by the graph of y = 240x?

• Direct variation

• Constant variation

• Exponential growth

• Inverse variation