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

Front

What is the constant of proportionality?

Back

The constant of proportionality (k) in a direct variation equation y = kx represents the ratio of y to x. It is the factor by which x is multiplied to get y.

Front

Identify the equation of direct variation: y = 3x + 2 or y = 3x?

Back

y = 3x is a direct variation because it can be expressed in the form y = kx without any additional 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

If y = 5x, what is the constant of variation?

Back

The constant of variation is 5.

Front

Is the equation y = -2x a direct variation?

Back

Yes, y = -2x is a direct variation because it can be expressed in the form y = kx, where k = -2.

Front

What is the relationship between x and y in direct variation?

Back

In direct variation, as x increases, y increases proportionally, and as x decreases, y decreases proportionally.

Front

If y = 4 when x = 1, what is the constant of variation?

Back

The constant of variation is 4, since y = kx gives k = 4.

Front

Is the equation y = rac{1}{2}x a direct variation?

Back

Yes, y = rac{1}{2}x is a direct variation.

Front

What happens to y if x is doubled in a direct variation?

Back

If x is doubled, y will also double, maintaining the proportional relationship.