Inverse Variation Concepts and Problems

The video tutorial introduces the concept of inverse variation, where y varies inversely with x. It explains the equation y = k/x and demonstrates how to solve for the constant k using an example. The tutorial walks through the process of plugging in values, performing cross multiplication, and deriving the final equation. The lesson concludes with a summary of the steps involved in solving inverse variation problems.

What does it mean when y varies inversely with x?

• y decreases as x increases

• y and x are unrelated

• y remains constant as x changes

• y increases as x increases

Which of the following represents the equation for inverse variation?

• y = k + x

• y = kx

• y = k / x

• y = x / k

In the equation y = k / x, what does k represent?

• The slope of the line

• The constant of variation

• The x-intercept

• The y-intercept

If y is 3 when x is 6, what is the value of k?

• 18

• 9

• 24

• 12

How do you solve for k in the equation y = k / x?

• Multiply y and x

• Divide y by x

• Add y and x

• Subtract x from y

What is the final equation if k is found to be 18?

• y = 18x

• y = 18 / x

• y = x / 18

• y = x + 18

What is the purpose of substituting k back into the equation?

• To find the value of y

• To check if k is correct

• To find the value of x

• To form the complete inverse variation equation

What is the relationship between x and y in an inverse variation?

• Exponentially related

• Directly proportional

• Inversely proportional

• Unrelated

What happens to y if x is doubled in an inverse variation?

• y is squared

• y remains the same

• y is halved

• y is doubled

What is the key takeaway from the inverse variation problem discussed?

• The equation is y = kx

• y and x are directly proportional

• The relationship between y and x is inverse

• The value of k is always 1