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

If y varies directly with x and y = 10 when x = 2, what is the equation of variation?

Back

y = 5x.

Front

If y varies inversely with x and y = 3 when x = 4, what is the equation of variation?

Back

y = 12/x.

Front

What does the constant of variation represent in direct variation?

Back

The constant of variation (k) represents the ratio of y to x in direct variation, indicating how much y changes for a unit change in x.

Front

What does the constant of variation represent in inverse variation?

Back

The constant of variation (k) represents the product of x and y in inverse variation, indicating that as one variable increases, the other decreases.

Front

Identify the equation that represents direct variation: y = 3x + 2 or y = 4x.

Back

y = 4x.

Front

Identify the equation that represents inverse variation: y = 2/x or y = 5x.

Back

y = 2/x.

Front

If the ordered pairs (2, 8) and (4, 16) are given, do they represent direct variation?

Back

Yes, they represent direct variation because the ratio of y to x is constant (4).

Front

If y = 6 when x = 3, what is the value of y when x = 9 in direct variation?

Back

y = 18.