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Holt CA Course 1 7-9Direct Variation Warm Up Warm Up California Standards California Standards Lesson Presentation Lesson PresentationPreview

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Holt CA Course 1 7-9Direct Variation Warm Up Tell whether the ratios are proportional. 1. = 2. = 3. = 4. = yes yes no yes ? ? ? ?

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Holt CA Course 1 7-9Direct Variation AF4.2 Solve multistep problems involving rate, average speed, distance, and time or a direct variation. Also covered: AF3.3, AF3.4 California Standards

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Holt CA Course 1 7-9Direct Variation A direct variation is a linear function that can be written as y = kx, where k is a nonzero constant called the constant of variation.

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Holt CA Course 1 7-9Direct Variation Determine whether the data set shows direct variation. A. Additional Example 1: Determining Whether a Data Set Varies Directly

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Holt CA Course 1 7-9Direct Variation Method 1: Make a graph. Additional Example 1A Continued The graph is not linear.

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Holt CA Course 1 7-9Direct Variation Method 2: Compare ratios = ? ≠ 264 The ratios are not equivalent. Both methods show the relationship is not a direct variation. Additional Example 1A Continued

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Holt CA Course 1 7-9Direct Variation Determine whether the data set shows direct variation. B. Additional Example 1: Determining Whether a Data Set Varies Directly

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Holt CA Course 1 7-9Direct Variation Method 1: Make a graph. Additional Example 1B Continued Plot the points. The points lie in a straight line. (0, 0) is included.

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Holt CA Course 1 7-9Direct Variation Method 2: Compare ratios. Both methods show the relationship is a direct variation === Additional Example 1B Continued The ratio is constant.

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Holt CA Course 1 7-9Direct Variation Rachel rents space in a salon to cut and style hair. She paid the salon owner $24 for 3 cut and styles. Write a direct variation function for this situation. If Rachel does 7 cut and styles, how much will she pay the salon owner? Additional Example 2: Finding Equations of Direct Variation y = kx 24 = k 3 8 = k y = 8x Think: The amount owed varies directly with the amount of cuts given. Substitute 24 for y and 3 for x. Solve for k. Substitute 8 for k in the original equation. x = 3 and y = 24 Step 1 Write the direct variation function.

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Holt CA Course 1 7-9Direct Variation Step 2 Find how much Rachel will pay the salon owner for 7 cut and styles. Additional Example 2 Continued y = 8(7) y = 56 Substitute 7 for x in the direct variation function. Multiply. Rachel will pay the salon owner $56 for 7 cut and styles.

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Holt CA Course 1 7-9Direct Variation Mrs. Perez has $4000 in a CD and $4000 in a money market account. The amount of interest she has earned since the beginning of the year is organized in the following table. Determine whether there is a direct variation between either of the data sets and time. If so, find the equation of direct variation. Additional Example 3: Money Application

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Holt CA Course 1 7-9Direct Variation Additional Example 3 Continued A. interest from CD and time interest from CD time = 17 1 = = 17 interest from CD time 34 2 The second and third pairs of data result in a common ratio. In fact, all of the nonzero interest from CD to time ratios are equivalent to 17. The variables are related by a constant ratio of 17 to 1. = = = 17 interest from CD time =

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Holt CA Course 1 7-9Direct Variation Additional Example 3 Continued B. interest from money market and time interest from money market time = = interest from money market time = = ≠ 18.5 If any of the ratios are not equal, then there is no direct variation. It is not necessary to compute additional ratios or to determine whether (0, 0) is included.

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Holt CA Course 1 7-9Direct Variation Lesson Quiz: Part I Determine whether the data sets show direct variation direct variation Amount of Water in a Rain Gauge Time (h)12345 Rain (in) Driving Time Speed (mi/h) Time (h) no direct variation

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Holt CA Course 1 7-9Direct Variation Lesson Quiz: Part II 3. Roy’s income varies directly with the number of dogs that he walks. He earned $8.50 for walking 2 dogs. Write a direct variation function for this situation. If Roy walks 5 dogs, how much will he earn? y = 4.25x; $21.25

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