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 if a table represents Direct Variation?

Back

If a table represents Direct Variation, the ratio of the two variables (y/x) is constant for all pairs of values.

Front

How can you identify Direct Variation from a graph?

Back

A graph represents Direct Variation if it 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 non-zero constant that relates the two variables in a direct variation equation y = kx.

Front

If y varies directly with x, and y = 12 when x = 3, what is the constant of variation?

Back

k = y/x = 12/3 = 4.

Front

Does the following table represent direct variation? (x: 1, y: 2; x: 2, y: 4; x: 3, y: 6)

Back

Yes, the ratios (y/x) are all equal to 2.

Front

Does the following table represent direct variation? (x: 1, y: 3; x: 2, y: 5; x: 3, y: 7)

Back

No, the ratios (y/x) are not constant.

Front

What is an example of a real-world situation that demonstrates Direct Variation?

Back

The relationship between distance and time at a constant speed is an example of Direct Variation.

Front

If y = 5 when x = 1, what is y when x = 4 in a direct variation?

Back

y = kx; k = 5/1 = 5; y = 5 * 4 = 20.

Front

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

Back

The equation is y = 3x.