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 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 y = 16 when x = 32, what is the constant of variation (k)?

Back

k = y/x = 16/32 = 1/2.

Front

Is the equation y = 2x + 1 a direct variation?

Back

No, because it includes a constant term (1) that does not allow y to vary directly with x.

Front

What does it mean if y varies directly with x?

Back

It means that as x increases or decreases, y changes in direct proportion to x.

Front

If y = 3x, what is the constant of variation?

Back

The constant of variation (k) is 3.

Front

How can you tell if an equation represents direct variation?

Back

An equation represents direct variation if it can be written in the form y = kx, with no additional constant term.

Front

If y = (1/2)x, what happens to y if x is doubled?

Back

If x is doubled, y will also double, demonstrating direct variation.

Front

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

Back

In direct variation, the ratio of y to x is constant.

Front

If y = 4 when x = 8, what is the equation of direct variation?

Back

The equation is y = (1/2)x.