Direct Variation

Proportional Versus Nonproportional Functions: What are the Differences?

Copy and paste the following link into your browser to learn more about the differences between proportional and nonproportional functions: http://www.bing.com/videos/search?q=Proportional+and+Nonproportional+Functions&&view=detail&mid=D42CE73FBC5C229E7C97D42CE73FBC5C229E7C97&FORM=VRDGAR

Identifying Direct Variation

If a linear function is a direct variation, then it MUST have a CONSTANT OF VARIATION. Copy and paste the following link into your browser to learn more about identifying [verifying] direct variation: http://www.bing.com/videos/search?q=identifying+direct+variation&&view=detail&mid=3C50366A27DDCF7270CE3C50366A27DDCF7270CE&FORM=VRDGAR

Constant of Variation

The constant ratio between two variables quantities is called the CONSTANT OF VARIATION.

Proportion Linear Function

The graph of a direct variation, which is a PROPORTIONAL LINEAR RELATIONSHIP, is a line that passes through the origin [that is, it must pass through the 0, 0 coordinate on the graph. ➜ NOTE: If the line of the graph does NOT pass through the origin [0, 0 coordinate on the graph] then the graph CANNOT be a proportional linear relationship. Copy and paste the following link into your browser to learn more about identifying proportional linear function: http://www.bing.com/videos/search?q=proportional+linear+function&&view=detail&mid=62004B3FF2F67C0D48A362004B3FF2F67C0D48A3&FORM=VRDGAR

Solving a Direct Variation Using an Equation or a Proportion

Two methods can be used to solve a direct variation: [1] use an equation, or [2] use a proportion. For example, Let's assume that the age of a dog varies directly as its equivalent age in human years. That is, one year in a dog's life is equivalent to 21 in human years. ➜ METHOD # 1: USING AN EQUATION [1] Write an equation of direct variation where 'x' represents the actual age of the dog, and where 'y' represent the human-equvalent age: y = kx [2] Substituting y = 21 and x = 3, 21 = k(3) [3] Simplify: 7 = k [4] Substitute k = 7, then y = 7 • x [5] Use this equation to find y when x = 6: y = 7x, where x =6 y = 7 • 6 y = 42 ➜ METHOD # 2: USING A PROPORTION [1] Write a proportion showing human age equivalent for a dog divided by the dog's actual age in years: Human Equivalent Age / Actual Age: 21 / 3 = x / 3 [2] Find the cross products of this proportion: 21 • 6 = 3 • x [3] Multiply those products: 126 =3x [4] Divide each side by 3 [to isolate the variable]: 126 / 3 = 3x /3 [5] Simplify: 42 = x Using either method a dog that is six [6] actual is 42 years old in human-equivalent years.

Direct Variation

When two variable quantities have a constant ratio, then their relationship is called a DIRECT VARIATION. ➜ WORDS: Direct variation is a relationship in which the ratio of 'y' to 'x' is a constant value ['k']. In this relationship, 'y' varies DIRECTLY with 'x'. ➜ SYMBOLS: k = y/x, or y = k • x, where y ≠ x ➜ EXAMPLE y = 3x