Proportional/Nonproportional Equations

Front

What is a proportional relationship?

Back

A proportional relationship is one where two quantities maintain a constant ratio. If one quantity increases, the other increases at the same rate.

Front

What is a non-proportional relationship?

Back

A non-proportional relationship is one where the ratio between two quantities is not constant. One quantity may increase while the other does not.

Front

Example of a proportional relationship: If 3 pizzas cost $30, how much do 5 pizzas cost?

Back

5 pizzas cost $50. (The cost per pizza is constant.)

Front

Example of a non-proportional relationship: If a taxi charges a flat fee of $5 plus $2 per mile, is this proportional?

Back

No, it is non-proportional because of the flat fee.

Front

What is the equation for a proportional relationship?

Back

y = kx, where k is the constant of proportionality.

Front

What is the equation for a non-proportional relationship?

Back

y = mx + b, where b is not zero.

Front

If y = 3x + 2, is this a proportional relationship?

Back

No, because of the +2, which is a constant.

Front

If y = 4x, is this a proportional relationship?

Back

Yes, because it can be expressed as y = kx with k = 4.

Front

What does the slope represent in a proportional relationship?

Back

The slope represents the constant rate of change between the two quantities.

Front

How do you determine if an equation is proportional?

Back

Check if it can be written in the form y = kx without any constant added or subtracted.