Exploring Direct, Inverse, and Joint Variation

This video tutorial covers the concepts of direct, inverse, and joint variation in algebra. It explains how these variations represent relationships between variables, using constants of variation. The tutorial provides examples and practice problems to help students understand how to identify and work with these variations in equations.

What does it mean when 'y varies directly with x'?

• y = k + x

• y = k * x

• y = k / x

• y = k - x

If y = x / 3, how is this rewritten to show direct variation?

• y = x + 3

• y = x - 3

• y = 1/3 * x

• y = 3 * x

In the equation y = kx, if y = 8 when x = 4, what is k?

• 2

• 32

• 12

• 0.5

What is the constant of variation if y = 4 / x?

• 4

• 1/4

• x

• y

What indicates an inverse variation in the equation form?

• y = k - x

• y = k + x

• y = k / x

• y = k * x

If y varies inversely as x and y = 5 when x = 2, what is the constant k?

• 5

• 10

• 2.5

• 7.5

In a joint variation, if z = k * x * y and z = 20 when x = 2 and y = 5, what is k?

• 2

• 5

• 10

• 1

What does it mean if z varies jointly with x and y?

• z = k - (x + y)

• z = k + x + y

• z = k * x * y

• z = k / (x * y)

How do you determine if a table shows a direct variation?

• Divide y by x and check if the result varies

• Divide x by y and check if the result is constant

• Multiply x by y and check if the result is constant

• Add x to y and check if the result is constant

If a table shows x * y always equals 60, what type of variation is it?

• No variation

• Joint variation

• Inverse variation

• Direct variation