proportional or non-proportional

Front

What is a proportional relationship?

Back

A proportional relationship is one in which two quantities maintain a constant ratio, meaning 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 in which the ratio between two quantities is not constant, often represented by equations that include a constant term or do not pass through the origin.

Front

How can you identify a proportional relationship from an equation?

Back

An equation represents a proportional relationship if it can be expressed in the form y = kx, where k is a constant and there is no additional constant term.

Front

What does it mean if a graph does not pass through the origin?

Back

If a graph does not pass through the origin, it indicates a non-proportional relationship, as proportional relationships must pass through the point (0,0).

Front

What is the significance of the slope in a proportional relationship?

Back

In a proportional relationship, the slope represents the constant ratio between the two quantities, and it remains the same regardless of the values of x and y.

Front

Can a linear equation with a y-intercept be proportional?

Back

No, a linear equation with a y-intercept (other than zero) is non-proportional because it does not pass through the origin.

Front

What is the graphical representation of a proportional relationship?

Back

The graphical representation of a proportional relationship is a straight line that passes through the origin (0,0).

Front

What is the difference between direct variation and proportional relationships?

Back

Direct variation is a specific type of proportional relationship where one variable is a constant multiple of another, typically expressed as y = kx.

Front

How can you determine if a set of points represents a proportional relationship?

Back

To determine if a set of points represents a proportional relationship, check if the ratio of y to x is constant for all points.

Front

What is an example of a non-proportional equation?

Back

An example of a non-proportional equation is y = 2x + 3, as it includes a constant term (3) and does not pass through the origin.