Proportional Relationships and Conversions

The video tutorial covers the concept of ratios and proportional relationships using various examples, including shapes, trail mix, and scales. It explains how to use tables and equations to identify proportional relationships and compares these relationships using graphs. The tutorial also discusses the constant of proportionality and its significance in different contexts.

Which shape is different from the others based on their width-to-height ratios?

• Shape A

• Shape B

• Shape C

• Shape D

What is the constant of proportionality when mixing chocolate milk with 2 cups of milk and 3 tablespoons of syrup?

• 4/3

• 3/2

• 1/2

• 2/3

If a map uses a scale of 1 inch to 60 miles, what is the actual area of a park that measures 4 inches by 6 inches on the map?

• 720 square miles

• 1440 square miles

• 3600 square miles

• 2160 square miles

How long will it take a car traveling at 65 miles per hour to cover 97.5 miles?

• 1.75 hours

• 1.25 hours

• 1.5 hours

• 2 hours

What is the equation to convert kilometers to miles if 1 kilometer is approximately 0.621 miles?

• miles = kilometers * 0.621

• miles = kilometers + 0.621

• miles = kilometers / 0.621

• miles = kilometers - 0.621

Which of the following scenarios is an example of a non-proportional relationship?

• A rabbit running at a constant speed

• A fountain drink pricing based on volume

• A taxi service charging a fixed rate per mile

• A turtle running with a consistent ratio of distance to time

What is the constant of proportionality in the equation y = 1760m?

• 1 yard per 1760 miles

• 1 mile per 1760 yards

• 1760 yards per mile

• 1760 miles per yard

Which equation represents a proportional relationship?

• y = x - 7

• y = x^2

• y = 3x

• y = x + 5

In a graph of a proportional relationship, what does the constant of proportionality represent?

• The slope of the line

• The curvature of the line

• The x-intercept of the line

• The y-intercept of the line

If a graph shows a straight line passing through the origin, what does it indicate about the relationship?

• It is an exponential relationship

• It is a non-linear relationship

• It is a proportional relationship

• It is a quadratic relationship