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

Learn to recognize direct variation by graphing tables of data and checking for constant ratios.

Vocabulary direct variation constant of proportionality

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.

The constant of variation is also called the constant of proportionality. Reading Math

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

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

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

Additional Example 2A: 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 y varies directly with x. 54 = k  6 Substitute for x and y. 9 = k Solve for k. Substitute 9 for k in the original equation. y = 9x

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

Exit Ticket 11 11

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 = 26x y = x 1 9 y = x 6 5

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