Direct Variation

Front

What is direct variation?

Back

Direct variation is a relationship between two variables where one variable is a constant multiple of the other, expressed as y = kx, where k is a non-zero constant.

Front

What does it mean if a situation is proportional?

Back

A proportional situation means that the ratio between two quantities remains constant, and the graph of the relationship is a straight line that passes through the origin.

Front

What is the ordered pair that a direct variation always goes through when graphed?

Back

(0, 0)

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 varying ratios.

Front

If y varies directly with x, what is the equation that represents this relationship?

Back

y = kx, where k is the constant of variation.

Front

What is the constant of variation in a direct variation equation?

Back

The constant of variation (k) is the ratio of y to x in the equation y = kx.

Front

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

Back

If the ratio of y to x is constant for all pairs of data, then the relationship is proportional.

Front

What does a graph of a proportional relationship look like?

Back

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

Front

What is an example of a non-proportional relationship?

Back

An example of a non-proportional relationship is y = 2x + 3, which does not pass through the origin.

Front

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

Back

If the ratios of y to x are not constant across the table, the relationship is non-proportional.