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 constant of variation in direct variation?

Back

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

Front

If y varies directly with x, and y = 10 when x = 2, what is the value of k?

Back

k = y/x = 10/2 = 5.

Front

Does a direct variation have a y-intercept other than zero?

Back

No, a direct variation always has a y-intercept of zero.

Front

What is the equation of a direct variation if k = 3?

Back

The equation is y = 3x.

Front

If y = 4 when x = 1, does this represent a direct variation?

Back

Yes, because the ratio y/x = 4/1 = 4 is constant.

Front

What is the slope of the line in a direct variation?

Back

The slope of the line in a direct variation is equal to the constant of variation (k).

Front

How can you tell if a table represents a direct variation?

Back

A table represents a direct variation if the ratio of y to x is constant for all pairs of values.

Front

What does it mean if a graph does not pass through the origin?

Back

If a graph does not pass through the origin, it does not represent a direct variation.