Proportional Relationships and Constants

The video tutorial introduces seventh graders to proportional relationships, focusing on identifying constants in ordered pairs and using them to determine proportionality. Through examples involving snowfall, candy cost, typing speed, and square area, students learn to calculate and verify proportional relationships using the formula y = kx, where k is the constant. The tutorial emphasizes the importance of consistent constants across data points to establish proportionality.

What is a key requirement for a relationship to be considered proportional?

• The values of x and y must be equal.

• All ordered pairs must have different constants.

• The constant of proportionality must be the same for all ordered pairs.

• The equation must be in the form of y = x + k.

How do you find the constant of proportionality in a table?

• By adding x and y values.

• By multiplying x and y values.

• By dividing y by x for each ordered pair.

• By subtracting x from y.

In Example 1, why was the relationship not proportional?

• The x values were not consistent.

• The y values were not consistent.

• The table had missing values.

• The constant of proportionality was not the same for all ordered pairs.

What was the constant rate at which Bella typed?

• 30 words per minute

• 42 words per minute

• 60 words per minute

• 50 words per minute

How can you determine if Bella's typing speed is proportional to the time she types?

• By adding the number of words and the number of minutes.

• By checking if the number of words typed is always 42 times the number of minutes.

• By ensuring the number of words typed is equal to the number of minutes.

• By dividing the number of words by the number of minutes.

What equation represents Bella's typing speed as a proportional relationship?

• y = x/42

• y = 42 + x

• y = 42x

• y = x - 42

In Example 3, what formula is used to find the area of a square?

• Length times width

• Side times side

• Diameter times radius

• Base times height

Why was the relationship between the side length and area of a square not proportional?

• The side lengths were not equal.

• The area was not calculated correctly.

• The table was incomplete.

• The constant of proportionality was different for each pair.

What is the constant of proportionality in a proportional relationship?

• The sum of x and y values

• The difference between x and y values

• The ratio of y to x

• The product of x and y values

What must be true for a table of values to represent a proportional relationship?

• The constant of proportionality must be the same for all ordered pairs.

• The y values must be greater than the x values.

• The x values must be greater than the y values.

• The table must have an even number of rows.