Proportional vs. 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. The graph of a proportional relationship passes through the origin (0,0).

Front

What is a non-proportional relationship?

Back

A non-proportional relationship is one in which the ratio between two quantities is not constant. This means that the relationship does not maintain a consistent rate of change, and the graph does not pass through the origin.

Front

How can you identify a proportional relationship from a table of values?

Back

A proportional relationship can be identified in a table of values if the ratios of corresponding values (y/x) are constant for all pairs of values.

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 that the relationship is non-proportional, as there is a y-intercept that is not zero.

Front

What is the significance of the y-intercept in determining proportionality?

Back

In a proportional relationship, the y-intercept is always zero. If the y-intercept is not zero, the relationship is non-proportional.

Front

What is the y-intercept of the equation y = mx + b?

Back

In the equation y = mx + b, 'b' represents the y-intercept, which is the value of y when x is zero.

Front

How do you determine if a linear equation represents a proportional relationship?

Back

A linear equation represents a proportional relationship if it can be expressed in the form y = mx, where m is a non-zero constant. If there is an additional constant (b) added, the relationship is non-proportional.

Front

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

Back

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

Front

Can a non-proportional relationship have a positive slope?

Back

Yes, a non-proportional relationship can have a positive slope, but it will also have a non-zero y-intercept, indicating that it does not pass through the origin.

Front

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

Back

An example of a proportional relationship is the relationship between distance and time when traveling at a constant speed; as time increases, distance increases at a constant rate.