Exploring the Constant of Proportionality from Graphs

The video tutorial explains the concept of proportional relationships and the constant of proportionality. It begins by introducing the idea of proportionality between variables y and x, and then defines the constant of proportionality as the number that multiplies x to yield y. The tutorial uses a table to demonstrate how to calculate this constant, showing that when x is 1, y is 3, and when x is 2, y is 6, leading to a constant of 3. Finally, it verifies the relationship by deriving the equation y = 3x, confirming that 3 is the constant of proportionality.

What does a proportional relationship between two variables imply?

• One variable is always the square of the other.

• The variables increase at different rates.

• There is a constant rate of change between the variables.

• The variables are unrelated.

What is the constant of proportionality?

• The difference between two variables.

• A variable that changes over time.

• The sum of two variables.

• A constant number that is multiplied by one variable to get the other.

What happens to y when x is 0 in a proportional relationship?

• y becomes 10

• y becomes 1

• y is undefined

• y also becomes 0

How can the constant of proportionality be determined from a table?

• By subtracting the y values from the x values.

• By multiplying the x values.

• By dividing y by x for any pair of values.

• By adding the x and y values.

If x is 2 and y is 6, what is the constant of proportionality?

• 2

• 3

• 4

• 6

In a proportional relationship, if x is doubled, what happens to y?

• y is quadrupled

• y is doubled

• y remains the same

• y is halved

What is the purpose of creating a table when finding the constant of proportionality?

• To visualize the relationship between x and y

• To add all the values of x and y

• To find the sum of x and y

• To divide x by y

What is the constant of proportionality in the equation y = 3x?

• 0

• y

• x

• 3

Which equation represents a proportional relationship with a constant of proportionality of 4?

• y = 4x

• y = x + 4

• y = x/4

• y = x - 4