2.5 Model Direct Variation

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Presentation transcript:

2.5 Model Direct Variation

In this lesson you will: Write direct variation equations.

Two variables show direct variation provided y=kx and k is not 0. K is called the constant of variation and y is said to vary directly with x. The graph of y = kx is a line through the origin. The variables x and y at the right vary directly, and y=12 when x=4. Write an equation relating x and y. Find y when x is 5. (5,15) (4,12) Note: In direct variation the ratio y/x is constant.

Does the data show a direct variation between x and y? This data shows information about 14-karat Gold Chains (1 gram per inch) Length, x (inches) 16 18 20 24 30 Price, y (dollars) 288 324 360 432 540 Does the data show a direct variation between x and y? To decide if there is a direct variation, check whether the quotient of y and x is constant. Yes, the data shows direct variation and the direct variation equation is y = 18x.

Does the data show direct variation? Loose Diamonds (round, colorless, very small flaws) Weight, x (carats) 0.5 0.7 1.0 1.5 2.0 Price, y (dollars) 2250 3430 6400 11,000 20,400 Does the data show direct variation?