Proportional Relationships

Front

What is a proportional relationship?

Back

A proportional relationship is a relationship between two quantities where the ratio of one quantity to the other is constant.

Front

What is the formula for a proportional relationship?

Back

The formula for a proportional relationship is y = kx, where k is the constant of proportionality.

Front

What does the slope (m) represent in the equation y = mx + b?

Back

The slope (m) represents the rate of change between the two variables.

Front

What is the significance of the y-intercept (b) in the equation y = mx + b?

Back

The y-intercept (b) is the value of y when x is 0, indicating where the line crosses the y-axis.

Front

How can you determine if a relationship is proportional from a graph?

Back

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

Front

What does it mean if the rates of change are constant?

Back

If the rates of change are constant, it means that the relationship between the two variables does not change as the values increase or decrease.

Front

What does it mean if the rates of change are variable?

Back

If the rates of change are variable, it means that the relationship between the two variables changes as the values increase or decrease.

Front

How do you find the rate of change from a table of values?

Back

To find the rate of change, divide the change in y by the change in x between two points: rate of change = (y2 - y1) / (x2 - x1).

Front

What is an example of a non-proportional relationship?

Back

An example of a non-proportional relationship is y = mx + b where b ≠ 0, indicating it does not pass through the origin.

Front

What is the difference between proportional and non-proportional relationships?

Back

Proportional relationships pass through the origin and have a constant ratio, while non-proportional relationships do not pass through the origin and have a variable ratio.