CFU: Direct, Inverse, Joint 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, expressed as y = kx, where k is the constant of variation.

Front

What is inverse variation?

Back

Inverse variation is a relationship between two variables where the product of the two variables is a constant, expressed as y = k/x, where k is the constant of variation.

Front

What does the constant k represent in direct and inverse variation?

Back

The constant k represents the constant of variation, which is the proportionality factor in direct and inverse relationships.

Front

How do you find the constant k in a direct variation problem?

Back

To find the constant k in a direct variation problem, use the formula k = y/x, where y is the value of the dependent variable and x is the value of the independent variable.

Front

How do you find the constant k in an inverse variation problem?

Back

To find the constant k in an inverse variation problem, use the formula k = xy, where x and y are the values of the two variables.

Front

What is the equation for inverse variation?

Back

The equation for inverse variation is y = k/x, where k is the constant of variation.

Front

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

Back

The equation of the variation is y = 5x.

Front

If y varies inversely with x and y = 20 when x = 4, what is the equation of the variation?

Back

The equation of the variation is y = 80/x.

Front

What is the relationship between speed and time in inverse variation problems?

Back

In inverse variation problems, as one variable (e.g., speed) increases, the other variable (e.g., time) decreases, and vice versa.

Front

How do you solve for y in a direct variation problem?

Back

To solve for y in a direct variation problem, use the equation y = kx, substituting the known values of k and x.