Proportional Relationships and Constants

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 C

• Shape D

• Shape B

• Shape A

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

• 1/2

• 3/2

• 2/3

• 3/4

What is the scale factor if a polygon is enlarged from 5 square units to 45 square units?

• 2

• 4

• 5

• 3

If a map uses a scale of 1 inch to 20 miles, what is the equivalent scale in inches to miles?

• 1 inch to 10 miles

• 1 inch to 20 miles

• 1 inch to 50 miles

• 1 inch to 100 miles

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

• 1.5 hours

• 1 hour

• 2 hours

• 2.5 hours

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

• A store sells apples at a constant price per pound.

• A taxi service charges a flat rate for the first mile and a different rate for each additional mile.

• A car travels at a constant speed of 60 miles per hour.

• A recipe requires twice as much sugar as flour.

What is the constant of proportionality in a table where each value of y is 7 times the corresponding value of x?

• 10

• 5

• 12

• 7

In a race, a turtle runs at a constant speed. If the turtle covers 54 meters in 1 minute, what is the equation representing the distance D in terms of time T?

• D = 54T

• D = 54 - T

• D = T/54

• D = 54 + T

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

• The relationship is proportional.

• The relationship is non-linear.

• The relationship is undefined.

• The relationship is inverse.

A recipe calls for 4 cups of raisins for every 6 cups of peanuts. What is the constant of proportionality when expressing peanuts in terms of raisins?

• 2/3

• 2

• 3/2

• 1/2