Understanding Rates and Proportional Relationships

The video tutorial covers proportional relationships and slope, starting with a warmup on unit rates and proportional relationships. It compares entrance fees at two national parks, explores graphing and slope, and interprets slope and unit rate in various contexts. The tutorial concludes with real-life examples of proportional relationships, emphasizing their applications.

What is a key characteristic of a proportional relationship?

• It must have a negative slope.

• It must have a slope of zero.

• It must pass through the origin (0,0).

• It must pass through the point (1,1).

If Arches National Park charges $25 per vehicle, how much would it cost for 3 vehicles?

• $50

• $75

• $125

• $100

How many songs can Marcus download in 3 minutes if he downloads 2 songs per minute?

• 8 songs

• 5 songs

• 6 songs

• 4 songs

What does the slope of a line represent in a proportional relationship?

• The minimum value of x

• The maximum value of y

• The rate of change between two quantities

• The y-intercept of the line

If a cyclist rides at a constant speed represented by the equation y = 12x, how far will they travel in 2 hours?

• 12 miles

• 24 miles

• 36 miles

• 48 miles

What is the unit rate if an online music store charges $3.75 for 3 songs?

• $1.75 per song

• $1.00 per song

• $1.25 per song

• $1.50 per song

How many miles can a manatee swim in 1 hour if it swims 10 miles in 2 hours?

• 2 miles

• 3 miles

• 4 miles

• 5 miles

If a rabbit can cover a distance represented by y = 35x, what is its speed in miles per hour?

• 35 miles per hour

• 40 miles per hour

• 25 miles per hour

• 30 miles per hour

Which job pays more per hour if the current job pays $7.25 and the new job offers $7.95?

• Current job

• New job

• Both pay the same

• Cannot be determined

What is the slope of a line if it represents a change of 200 units in y for every 1 unit in x?

• 250

• 200

• 150

• 100