Direct and Inverse Variation Review

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

How do you determine if a graph represents direct variation?

Back

A graph represents direct variation if it is a straight line that passes through the origin (0,0).

Front

How do you determine if a graph represents inverse variation?

Back

A graph represents inverse variation if it is a hyperbola that approaches the axes but never touches them.

Front

What is the constant of variation in direct variation?

Back

The constant of variation in direct variation is the ratio of y to x (k = y/x).

Front

What is the constant of variation in inverse variation?

Back

The constant of variation in inverse variation is the product of x and y (k = xy).

Front

If the time to complete a task varies inversely with the number of workers, what happens if you double the number of workers?

Back

If you double the number of workers, the time to complete the task is halved.

Front

Given the equation y = 3x, what happens to y if x is tripled?

Back

If x is tripled, y will also triple, resulting in y = 9x.

Front

If sales vary directly with attendance and sales are $15,000 when attendance is 500, what are the sales when attendance is 1,000?

Back

Sales will be $30,000.