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.

Tags

CCSS.HSF-LE.A.1B

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.

Tags

CCSS.HSF-LE.A.1B

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.