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 the graph of a direct variation look like?

Back

The graph of a direct variation is a straight line that passes through the origin (0,0).

Front

What is the equation for direct variation?

Back

The equation for direct variation is y = kx, where k is the constant of variation.

Front

If y varies directly with x and k = 2, what is the equation?

Back

The equation is y = 2x.

Front

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

Back

A relationship is a direct variation if the ratio of y to x is constant (y/x = k).

Front

What is the constant of variation in the equation y = 3x?

Back

The constant of variation is 3.

Front

Is the relationship y = 1/2x a direct variation?

Back

Yes, it is a direct variation because it can be expressed in the form y = kx.

Front

What does it mean if a graph is proportional?

Back

A graph is proportional if it represents a direct variation, meaning it is a straight line through the origin.

Front

If y = 4 when x = 2, what is the constant of variation?

Back

The constant of variation k is 2, since k = y/x = 4/2.

Front

Can a direct variation have a negative constant of variation?

Back

Yes, a direct variation can have a negative constant, which means the line will slope downwards.