Exploring Direct and Inverse Variation in Algebra

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

• y is equal to a constant multiplied by x

• y is equal to a constant divided by x

• y is equal to the sum of a constant and x

• y is equal to the difference between a constant and x

Which equation represents a direct variation?

• y = 3x

• y = 3/x

• y = x - 3

• y = x + 3

If y = 2x and x is doubled, what happens to y?

• y is quadrupled

• y remains the same

• y is halved

• y is doubled

What is the result of scaling down x by a factor of 3 in the equation y = -3x?

• y becomes zero

• y is scaled up by a factor of 3

• y is scaled down by a factor of 3

• y remains unchanged

What does it mean when we say 'y varies inversely with x'?

• y is equal to a constant multiplied by x

• y is equal to the difference between a constant and x

• y is equal to a constant divided by x

• y is equal to the sum of a constant and x

Which equation represents an inverse variation?

• y = x - 3

• y = x + 3

• y = 3x

• y = 3/x

If y = 2/x and x is doubled, what happens to y?

• y is halved

• y is doubled

• y remains the same

• y is quadrupled

What is the result of scaling up x by a factor of 2 in the equation y = 1/x?

• y is scaled down by a factor of 2

• y is scaled up by a factor of 2

• y becomes zero

• y remains unchanged

If y = 1/3x and x is tripled, what happens to y?

• y is tripled

• y is halved

• y is divided by 3

• y remains the same

In the context of inverse variation, if xy = 2 and x is doubled, what happens to y?

• y is doubled

• y is quadrupled

• y is halved

• y remains the same