4.5 Proportional Relationships

Front

What is a proportional relationship?

Back

A proportional relationship is a relationship between two quantities where the ratio of one quantity to the other quantity is constant.

Front

What is the constant of proportionality?

Back

The constant of proportionality is the constant value (k) that relates two proportional quantities, often represented as y = kx.

Front

If y = 3x, what is the constant of proportionality?

Back

k = 3.

Front

How do you determine if a relationship is proportional from a graph?

Back

A relationship is proportional if the graph is a straight line that passes through the origin (0,0).

Front

What does the equation y = 30x represent in a real-world context?

Back

It represents a situation where for every unit increase in x, y increases by 30, such as a cost that increases at a constant rate.

Front

If a job pays $56 for 8 hours of work, how do you find the pay per hour?

Back

Divide the total pay by the number of hours: $56 ÷ 8 hours = $7 per hour.

Front

What is the equation for a proportional relationship if the constant of proportionality is 9?

Back

y = 9x.

Front

True or False: The equation y = 30x can represent a dog kennel's daily boarding rate if it charges $30 per day.

Back

True.

Front

If a table shows values of x and y where y = 1/3x, what does this indicate?

Back

It indicates that for every 3 units of x, y increases by 1 unit, showing a proportional relationship.

Front

What is the significance of the origin (0,0) in proportional relationships?

Back

The origin represents the point where both quantities are zero, indicating that if one quantity is zero, the other must also be zero.