1. Warm Up Solve each proportion. = = 1. b = 10 2. y = 8 = = 3. 4. m = 5230 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

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

3. Vocabulary
direct variation
constant of proportionality

4. 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.

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

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

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

8. 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.

9. 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

10. 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

11. Exit Ticket 11 11

12. 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

13. 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