Direct Variation Concepts and Problems

The video tutorial explains the concept of direct variation, where y varies directly with x, meaning their constant is equal. It demonstrates setting up and solving the equation using proportions and the cross product method. The example provided shows how to find the value of x when given certain values of y and x, concluding with a solution of x equals 3/5.

What does it mean when y varies directly with x?

• y decreases as x increases

• y is inversely proportional to x

• y increases as x increases

• y is always greater than x

What happens to y if x is doubled in a direct variation?

• y is doubled

• y remains the same

• y is tripled

• y is halved

What is the relationship between y and x in a direct variation?

• y is unrelated to x

• y is equal to x

• y is directly proportional to x

• y is inversely proportional to x

In a direct variation, what remains constant?

• The ratio of y to x

• The difference between y and x

• The product of y and x

• The sum of y and x

If y = 2 when x = 4, what is the constant of variation?

• 1/2

• 2

• 4

• 8

If y = 6 and x = 2, what is the value of k in y = kx?

• 3

• 2

• 4

• 1

How can you express the relationship in a direct variation?

• y = k - x

• y = x - k

• y = kx

• y = x + k

What does the equation y = kx represent?

• A linear equation

• A quadratic equation

• An exponential equation

• A logarithmic equation

In the equation y = kx, what does k represent?

• The x-intercept

• The y-intercept

• The constant of variation

• The slope

What is the purpose of setting y/x equal to y/x in direct variation?

• To find the sum of y and x

• To find the difference between y and x

• To establish a proportion

• To solve for y