Proportional vs. non proportional

Front

What is a proportional relationship?

Back

A proportional relationship is one where two quantities maintain a constant ratio or rate. For example, if you double one quantity, the other quantity also doubles.

Front

What is a non-proportional relationship?

Back

A non-proportional relationship is one where the ratio between two quantities is not constant. For example, if one quantity increases but the other does not, or increases at a different rate.

Front

How can you identify a proportional relationship on a graph?

Back

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

Front

What does the y-intercept represent in a graph?

Back

The y-intercept is the point where the graph crosses the y-axis. It represents the value of y when x is 0.

Front

If a graph has a y-intercept of 3, is it proportional?

Back

Not necessarily. A graph can have a y-intercept of 3 and still be non-proportional if it does not pass through the origin.

Front

What is the equation of a proportional relationship?

Back

The equation of a proportional relationship can be written as y = kx, where k is the constant of proportionality.

Front

What is the equation of a non-proportional relationship?

Back

The equation of a non-proportional relationship can be written as y = mx + b, where b is the y-intercept and m is the slope.

Front

Give 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.

Front

Give an example of a non-proportional relationship in real life.

Back

An example of a non-proportional relationship is the relationship between the number of hours worked and the total pay if there is a fixed salary plus overtime.

Front

What happens to the graph of a proportional relationship if the constant of proportionality increases?

Back

If the constant of proportionality increases, the slope of the line on the graph becomes steeper.