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direct variation

A situation when one value increases as the other vaule increases or as one decreases the other decreases. y = kx k≠0

Inverse Variation

A situation when one value increases and the other value decreases. y = k/x k≠0

Real world situations

1st quadrant.

Step 1: y= k/x

Suppose that x and y vary inversely and x=3 when y= -5. What is the function?

Direct indications

Both x and y values increasing or decreasing. There is a clear pattern of x to y, or y to x. State the direct variation in the form of

Inverse indications

If you multiply x and y to get the same k, it is inverse.

Neither

If none of the other indicators work, it is not constant. Therefore it is neither.

Combined Variation

Combines direct and inverse for more complex relationships. For these you'll just plug in values most likely.

y=kx^2

y varies directly with square of x

y=k/x^3

y varies inversely with cubed of x

y=kxy

z varies jointly with x and y

y=kxy/w

z varies jointly with x and y and inversely with w

direct variation

If gummy bears cost $3.50 per pound, how much will 6 pounds cost? How much would a half a pound cost?