Proportional vs Non-Proportional

Front

What is a proportional relationship?

Back

A proportional relationship is one in which two quantities maintain a constant ratio. This means that as one quantity increases or decreases, the other does so in a consistent manner.

Front

What is a non-proportional relationship?

Back

A non-proportional relationship is one where the ratio between two quantities is not constant. This often involves a fixed value added or subtracted, leading to a linear equation of the form y = mx + b.

Front

Identify the equation of a proportional relationship.

Back

y = mx, where m is the constant of proportionality.

Front

Identify the equation of a non-proportional relationship.

Back

y = mx + b, where b is a non-zero constant.

Front

What does the 'b' represent in the equation y = mx + b?

Back

The 'b' represents the y-intercept, which is the value of y when x is zero.

Front

How can you tell if a graph represents a proportional relationship?

Back

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

Front

How can you tell if a graph represents a non-proportional relationship?

Back

A graph represents a non-proportional relationship if it does not pass through the origin or has a y-intercept that is not zero.

Front

What is the constant of proportionality?

Back

The constant of proportionality is the ratio of y to x in a proportional relationship, represented by 'm' in the equation y = mx.

Front

Give an example of a proportional situation.

Back

If you buy 3 apples for $6, the cost per apple is constant at $2, which is a proportional relationship.

Front

Give an example of a non-proportional situation.

Back

If you pay a $5 fee plus $2 for each apple, the total cost is not proportional to the number of apples.