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**Direct Variation and Proportion**

Objective: Write and apply direct variation and proportion problems

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Direct Variation The variable y varies directly as x if there is a nonzero constant k such that y = kx. The equation y = kx is called a direct variation equation and the number k is called the constant of variation.

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Example 1 Find the constant of variation, k and the direct variation equation if y varies directly as x and y = -24 when x = 4.

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Example 1 Find the constant of variation, k and the direct variation equation if y varies directly as x and y = -24 when x = 4. Use the direct variation equation Substitute -24 for y and 4 for x

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Example 1 Find the constant of variation, k and the direct variation equation if y varies directly as x and y = -24 when x = 4. Use the direct variation equation Substitute -24 for y and 4 for x Solve for k.

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Example 1 Find the constant of variation, k and the direct variation equation if y varies directly as x and y = -24 when x = 4. Use the direct variation equation Substitute -24 for y and 4 for x Solve for k. The direct variation equation is

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Try This Find the constant of variation, k and the direct variation equation if y varies directly as x and y = 21 when x = 7.

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Try This Find the constant of variation, k and the direct variation equation if y varies directly as x and y = 21 when x = 7. Use the direct variation equation Substitute 21 for y and 7 for x Solve for k. The direct variation equation is

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Example 2 Each day John rides his bike for exercise. When traveling at a constant rate, he rides 4 miles in about 20 minutes. At this rate, how long would it take John to travel 7 miles?

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Example 2 Each day John rides his bike for exercise. When traveling at a constant rate, he rides 4 miles in about 20 minutes. At this rate, how long would it take John to travel 7 miles?

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Example 2

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**Proportions A ratio is a comparison of two numbers by division.**

A proportion is a statement that two ratios are equal.

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**Proportions A ratio is a comparison of two numbers by division.**

A proportion is a statement that two ratios are equal. A proportion of the form can be rearranged like this:

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**Cross-Product Property**

The result of what we just did is called the cross-product property of proportions. This is also called the means-extremes product property.

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Physics Application

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Example 3

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Example 3

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Example 3

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Example 4

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Example 4

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Class work In pairs/groups Page 33 8-13

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Homework Pages 33-34 15-25 odd 37-51 odd

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

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

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