2.3 - Direct Variation.

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Presentation transcript:

2.3 - Direct Variation

Direct Variation A linear function defined by an equation of the form y = kx, where k ≠ 0, represents direct variation.

Constant of Variation The Slope, k, is constant. It can be represented at the ratio of

Identifying Direct Variation from a Table Determine whether y varies directly with x. If so, find the constant of variation and write the equations. 1. 2. X Y 2 8 3 12 5 20 X Y 1 4 2 7 5 16

You Try!! Determine whether y varies directly with x. If so, find the constant of variation and write the equations. 1. 2. X Y -1 -2 3 4 6 7 X Y -6 -2 3 1 12 4

Identifying Direct Variation from an Equation For each function, determine whether y varies directly with x. If so, find the constant of variation: y = 4x 2y = 3x y = 2x + 3

You Try!! Determine whether y varies directly with x. If so, find the constant of variation. y = x/2 2y – 1 = x 4x = 8y 7x + 4y = 10

Using Proportions If we know that y varies directly with x. We can use proportions to find missing information. Ex. Suppose y varies directly with x, and x = 3 when y = 7. Find x when y = 21.

You Try! y varies directly with x: If y = 25 when x = 15, find x when y = 10 If y = 30 when x = -3, find y when x = -9

Writing Equations Write an equation of the direct variation that includes the point (10, -15). You Try: Write an equation of the direct variation that includes the point (-40, 16).

Word Problems A dripping faucet wastes a cup of water if it drips for three minutes. The amount of water wasted varies directly with the amount of time the faucet drips. Find the constant of variation, and write an equation.

Word Problems The Height of an object varies directly with the length of its shadow. A person 6 ft tall casts an 8.5 ft shadow, while a tree casts a 38 ft shadow. How tall is the tree?

Word Problem The amount of a persons paycheck p varies directly with the numbers of hours worked t. For 4o hours of work, the paycheck is $390. Write an equation for the relationship between hours worked and pay.

Homework Pg. 74-75: 2-28 even