12 5 Direct Variation Warm Up Solve each

12 -5 Direct Variation Learn to recognize direct variation by graphing tables of data

12 -5 Direct Variation Vocabulary direct variation constant of proportionality

12 -5 Direct Variation A direct variation is a linear function that can be

12 -5 Direct Variation Reading Math The constant of variation is also called the

12 -5 Direct Variation Additional Example 1 A: Determining Whether a Data Set Varies

12 -5 Direct Variation Additional Example 1 A Continued Make a graph that shows

12 -5 Direct Variation Additional Example 1 A Continued You can also compare ratios

12 -5 Direct Variation Additional Example 2 A: Finding Equations of Direct Variation Find

12 -5 Direct Variation Additional Example 2 B: Finding Equations of Direct Variation x

12 -5 Direct Variation Exit Ticket Find each equation of direct variation, given that

12 -5 Direct Variation Exit Ticket 4. The table shows the amount of money

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12 -5 Direct Variation Warm Up Solve each proportion. 1. 3 = b 9 30 3. p = 4 9 12 b = 10 y = 56 2. 5 35 y=8 p=3 4. 28 = 56 m = 52 26 m

12 -5 Direct Variation Learn to recognize direct variation by graphing tables of data and checking for constant ratios.

12 -5 Direct Variation Vocabulary direct variation constant of proportionality

12 -5 Direct 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.

12 -5 Direct Variation Reading Math The constant of variation is also called the constant of proportionality.

12 -5 Direct Variation Additional Example 1 A: Determining Whether a Data Set Varies Directly Determine whether the data set shows direct variation.

12 -5 Direct Variation Additional Example 1 A Continued Make a graph that shows the relationship between Adam’s age and his length. The graph is not linear.

12 -5 Direct Variation Additional Example 1 A Continued You can also compare ratios to see if a direct variation occurs. 22 ? 27 3 = 12 81 81 ≠ 264 The ratios are not proportional. The relationship of the data is not a direct variation.

12 -5 Direct Variation Additional Example 2 A: Finding Equations of Direct Variation Find each equation of direct variation, given that y varies directly with x. y is 54 when x is 6 y = kx 54 = k 6 y varies directly with x. Substitute for x and y. 9=k Solve for k. y = 9 x Substitute 9 for k in the original equation.

12 -5 Direct Variation Additional Example 2 B: Finding Equations of Direct Variation x is 12 when y is 15 y = kx 15 = k 5=k 4 y = 5 x 4 y varies directly with x. 12 Substitute for x and y. Solve for k. 5 Substitute 4 for k in the original equation.

12 -5 Direct Variation Exit Ticket

12 -5 Direct Variation Exit Ticket Find each equation of direct variation, given that y varies directly with x. 1. y is 78 when x is 3. 2. x is 45 when y is 5. 3. y is 6 when x is 5. y = 26 x y =1 x 9 y =6 x 5

12 -5 Direct Variation Exit Ticket 4. The table shows the amount of money Bob makes for different amounts of time he works. Determine whethere is a direct variation between the two sets of data. If so, find the equation of direct variation; y = 12 x