Identify Proportional and Non-Proportional Relationships

What is a proportional relationship?

• A relationship where one quantity is always greater than the other.

• A relationship where the ratio of one quantity to the other is constant.

• A relationship that changes over time without a fixed ratio.

• A relationship that only applies to whole numbers.

What is the role of the constant of proportionality?

• It is the factor by which one quantity is multiplied to obtain the other in a proportional relationship.

• It represents the sum of two quantities in a relationship.

• It is the average of two quantities in a proportional relationship.

• It indicates the maximum value of a proportional relationship.

What is the equation of a proportional relationship?

• y = kx, where k is a constant

• y = k + x, where k is a constant

• y = k/x, where k is a constant

• y = x^2, where k is a constant

How can you identify a proportional relationship from an equation?

• If the equation can be rewritten in the form y = kx without any additional constants.

• If the equation contains a constant term that is not zero.

• If the equation has a variable that is squared.

• If the equation includes both x and y terms with different coefficients.

How can you determine if a table represents a proportional relationship?

• A table represents a proportional relationship if the ratios of corresponding values are constant.

• A table represents a proportional relationship if the values are all whole numbers.

• A table represents a proportional relationship if the first column is always greater than the second.

• A table represents a proportional relationship if the values increase by the same amount each time.

What is the significance of the y-intercept in a linear equation?

• The y-intercept indicates the value of y when x is zero; in a proportional relationship, the y-intercept is always zero.

• The y-intercept represents the slope of the line.

• The y-intercept is the point where the line crosses the x-axis.

• The y-intercept shows the maximum value of y in the equation.

How do you convert a non-proportional equation to a proportional one?

• By adding constant terms to the equation

• By eliminating any constant terms that do not allow the equation to pass through the origin

• By multiplying both sides of the equation by a constant

• By changing the variable names in the equation

What is the difference between direct variation and proportional relationships?

• Direct variation is a specific type of proportional relationship where one variable is a constant multiple of another.

• Direct variation means that two variables are always equal to each other.

• Proportional relationships can only be represented by linear equations.

• Direct variation occurs only when both variables are negative.

What is an example of a proportional relationship in real life?

• The relationship between distance and time at a constant speed.

• The relationship between the amount of water and the size of a container.

• The relationship between the number of hours worked and the total pay at varying rates.

• The relationship between temperature and the color of an object.

What is an example of a non-proportional relationship?

• The relationship between the number of items purchased and the total cost when there is a fixed fee.

• The relationship between distance and time at a constant speed.

• The relationship between the amount of water in a tank and the height of the water level.

• The relationship between the number of hours worked and the total pay at an hourly rate.