Understanding Proportional Relationships and Rates

The video tutorial covers the concept of using graphs and equations to represent proportional relationships. It explains the constant of proportionality and how to determine if a relationship is proportional by examining graphs. The tutorial includes examples such as the speed of a subway car and temperature changes over time to illustrate these concepts. Students are encouraged to practice identifying proportional relationships and understanding unit rates.

What is a proportion in mathematical terms?

• Two numbers that are equal

• Two equations that are equal

• Two variables that are equal

• Two fractions that are equal

In the context of the video, what does a constant rate of 60 miles per hour imply?

• The speed is constant over time

• The speed increases over time

• The speed varies with time

• The speed decreases over time

What does the constant of proportionality represent in a proportional relationship?

• The subtractive relationship between quantities

• The divisive relationship between quantities

• The additive relationship between quantities

• The multiplicative relationship between quantities

What is another term for the constant of proportionality?

• Inverse variation

• Direct variation

• Quadratic variation

• Linear variation

How can you determine if a graph represents a proportional relationship?

• If the graph has a positive slope

• If the graph is a curve

• If the graph passes through the origin

• If the graph is a straight line

If a graph of a relationship does not pass through the origin, what can be concluded?

• The relationship is quadratic

• The relationship is proportional

• The relationship is linear

• The relationship is not proportional

What is the unit rate of a subway car that travels 1 mile in 2 minutes?

• 2 miles per minute

• 0.25 miles per minute

• 0.5 miles per minute

• 1 mile per minute

How do you calculate the speed of a subway car from a graph?

• By finding the area under the line

• By finding the slope of the line

• By finding the y-intercept of the line

• By finding the x-intercept of the line

What happens to the temperature every half hour after midnight in the given example?

• It fluctuates randomly

• It decreases by 2 degrees

• It increases by 2 degrees

• It remains constant

What is the equation used to determine the temperature after a certain number of hours past midnight?

• y = 42 - 4x

• y = 42 - 2x

• y = 42 + 4x

• y = 42 + 2x