Inverse Variation and Proportionality

The video tutorial explains inverse variation, focusing on how y is inversely proportional to the square of x. It demonstrates finding the constant of proportionality, k, using given values of y and x. The tutorial then shows how to write the specific variation equation using the calculated k. Finally, it calculates y for a given x value, rounding the result to three decimal places.

What does it mean when y is inversely proportional to the square of x?

• y increases as x increases

• y decreases as x increases

• y is constant regardless of x

• y is directly proportional to x

Which equation represents y being inversely proportional to the square of x?

• y = k * x

• y = k / x

• y = k / x^2

• y = k * x^2

If y = 13 when x = 12, what is the first step to find the constant of proportionality k?

• Divide y by x

• Multiply y by x

• Add y and x

• Substitute y and x into the equation y = k / x^2

What is the value of k if y = 13 and x = 12?

• 13

• 12

• 1872

• 144

What is the specific inverse variation equation derived using k = 1872?

• y = 1872 * x

• y = 1872 / x

• y = 1872 / x^2

• y = 1872 * x^2

How do you find y when x = 45 using the equation y = 1872 / x^2?

• Add 1872 and 45

• Divide 1872 by 45

• Multiply 1872 by 45

• Divide 1872 by the square of 45

What is the approximate value of y when x = 45, rounded to three decimal places?

• 0.924

• 0.750

• 0.500

• 1.000

Why is it important to round the result to three decimal places?

• To make the number smaller

• To ensure precision in calculations

• To make the number larger

• To simplify the equation

What happens to y as x increases in the equation y = 1872 / x^2?

• y increases

• y decreases

• y becomes zero

• y remains constant

What is the role of the constant k in the inverse variation equation?

• It has no role

• It is the y-intercept

• It determines the slope of the line

• It is the constant of proportionality