Direct & Inverse 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 Inverse Variation?

Back

Inverse variation is a relationship between two variables where the product of the two variables is a constant. It can be expressed as y = k/x, where k is a non-zero constant.

Front

Identify the equation that represents Direct Variation: y = kx, y = k/x, y = x/k, y = mx + b

Back

y = kx

Front

Identify the equation that represents Inverse Variation: y = kx, y = k/x, y = x/k, y = mx + b

Back

y = k/x

Front

If y varies directly with x and y = 6 when x = 4, what is the constant of variation (k)?

Back

k = 1.5

Front

If y varies inversely with x and y = 8 when x = 4, what is the equation relating x and y?

Back

y = 32/x

Front

What does it mean if two variables vary directly?

Back

It means that as one variable increases, the other variable also increases, and vice versa.

Tags

CCSS.HSF-LE.A.1B

Front

What does it mean if two variables vary inversely?

Back

It means that as one variable increases, the other variable decreases, and vice versa.

Tags

CCSS.HSF-LE.A.1B

Front

If the height of a wave varies directly with time, and at 4 seconds the wave is 6 feet high, how high will it be at 6 seconds?

Back

The wave will be 9 feet high.

Front

If y = 2x + 3, does this represent direct variation?

Back

No, because it includes a constant term (3).