Proportional Relationships and Constants

This video tutorial covers the concept of proportional relationships, focusing on various examples such as sound levels, fountain drink costs, taxi fares, and race distances. It explains how to determine if relationships are proportional and how to calculate constants of proportionality. The video also discusses the scaling of a rectangle's dimensions and its diagonal.

Which of the following scenarios is NOT an example of a proportional relationship?

• The loudness of a sound based on distance

• The cost of a taxi ride per mile

• The distance a turtle runs over time

• The cost of fountain drinks at Hot Dog Hut

What is the cost of a taxi ride for 2 miles according to the pricing model discussed?

• $3.50

• $2.90

• $3.00

• $2.00

Why is the taxi service's pricing model not considered a proportional relationship?

• The cost per mile is constant.

• The initial cost is higher than subsequent costs.

• The ratio of price to distance is not consistent.

• The cost decreases with distance.

For the turtle's run, what is the equation that represents the proportional relationship between distance and time?

• d = 54 + t

• d = 54t

• d = t/54

• d = t + 54

What is the constant of proportionality for Table A?

• 5

• 10

• 7

• 12

Which table has a constant of proportionality of 120?

• Table C

• Table B

• Table D

• Table A

What is the reduced form of the ratio 3/75 in Table C?

• 1/25

• 1/15

• 1/30

• 1/20

What is the constant of proportionality for Table D?

• 2.5

• 3

• 3.5

• 2

If a rectangle's length and width are doubled, how does the diagonal change?

• It remains the same.

• It doubles.

• It triples.

• It quadruples.

Who is correct about the change in distance to the far corner when the field's dimensions are doubled?

• Both

• Neither

• Meyer

• Kieran