Understanding Direct and Inverse Variation

The video tutorial explains the differences between direct and inverse variations, focusing on how to determine the equations for each. Direct variation is characterized by both x and y values increasing or decreasing together, represented by the equation y = kx. Inverse variation involves x and y values moving in opposite directions, represented by y = k/x. The tutorial provides examples and methods to calculate the constant of variation (k) for both types, using tables to illustrate the concepts. It also discusses how to identify whether a table represents direct or inverse variation.

What is a key characteristic of direct variation in a table?

• Both x and y values increase or decrease together.

• x values increase while y values decrease.

• y values remain constant.

• x values remain constant.

Which equation represents direct variation?

• y = x + k

• y = kx

• y = k/x

• y = x - k

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How do you find the constant of variation (k) in direct variation?

• Subtract x from y.

• Add x and y values.

• Divide y by x.

• Multiply x and y values.

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What happens to y values in inverse variation when x values increase?

• y values remain constant.

• y values become zero.

• y values decrease.

• y values increase.

Which equation represents inverse variation?

• y = kx

• y = k/x

• y = x - k

• y = x + k

How do you find the constant of variation (k) in inverse variation?

• Multiply x and y values.

• Divide y by x.

• Add x and y values.

• Subtract x from y.

If x values increase and y values decrease, what type of variation is it?

• No variation

• Inverse variation

• Constant variation

• Direct variation

What indicates that a table does not represent direct variation?

• y values are constant.

• x and y values are equal.

• Different constants of variation for different x and y pairs.

• x values are constant.

What must be true for a table to represent direct or inverse variation?

• x values must be greater than y values.

• y values must be greater than x values.

• The constant of variation must be the same for all x and y pairs.

• x and y values must be equal.

What is a possible reason a table might not represent either direct or inverse variation?

• x and y values are negative.

• Different constants of variation for different x and y pairs.

• y values are all zero.

• x values are all zero.