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. It can be expressed as y = kx, where k is a non-zero constant.

Front

What does it mean for a graph to represent Direct Variation?

Back

A graph represents Direct Variation if it is a straight line that passes through the origin (0,0).

Front

How can you identify a Direct Variation graph among multiple options?

Back

Look for a straight line that passes through the origin. If the line does not pass through the origin, it is not a direct variation.

Front

What is a proportional relationship?

Back

A proportional relationship is one where two quantities maintain a constant ratio. In direct variation, the ratio of y to x is constant.

Front

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

Back

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

Front

What does it mean for a table to be proportional?

Back

A table is proportional if the ratios of the corresponding values in the two columns are constant.

Front

How can you determine if a relationship is a direct variation?

Back

Check if the ratio of y to x is constant and if the graph passes through the origin.

Front

What is the constant of variation in direct variation?

Back

The constant of variation (k) is the non-zero constant that relates the two variables in the equation y = kx.

Front

Can a relationship be both direct variation and proportional?

Back

Yes, all direct variations are proportional relationships, but not all proportional relationships are direct variations.

Front

What is an example of a direct variation equation?

Back

An example of a direct variation equation is y = 3x, where 3 is the constant of variation.