1. Direct Variation 88 Warm Up Use the point-slope form of each equation to identify a point the line passes through and the slope of the line. 1. y – 3 = – (x – 9) 2. y + 2 = (x – 5) 3. y – 9 = –2(x + 4) 4. y – 5 = – (x + 7) 1 7 2 3 1 4 Point: Slope:

2. Direct Variation 88 Vocabulary direct variation constant of proportionality Learn to recognize direct variation by graphing tables of data and checking for constant ratios.

3. Direct Variation 88 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

4. Direct Variation 88 Determine whether the data set shows direct variation. Additional Example 1A: Determining Whether a Data Set Varies Directly

5. Direct Variation 88 Make a graph that shows the relationship between Adam’s age and his length. The graph is not linear. Additional Example 1A Continued

6. Direct Variation 88 You can also compare ratios to see if a direct variation occurs. 22 3 27 12 = ? 81 264 81 ≠ 264 The ratios are not proportional. The relationship of the data is not a direct variation. Additional Example 1A Continued

7. Direct Variation 88 Find each equation of direct variation, given that y varies directly with x. y is 54 when x is 6 Additional Example 2A: Finding Equations of Direct Variation y = kx 54 = k  6 9 = k y = 9x y varies directly with x. Substitute for x and y. Solve for k. Substitute 9 for k in the original equation.

8. Direct Variation 88 x is 12 when y is 15 Additional Example 2B: Finding Equations of Direct Variation y = kx 15 = k  12 y varies directly with x. Substitute for x and y. Solve for k. = k 5 4 Substitute for k in the original equation. 5 4 y = x 5 4

9. Direct Variation 88 Lesson Quiz: Part I 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.

10. Direct Variation 88 Lesson Quiz: Part II 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.

11. Direct Variation 88 1. Identify the equation of direct variation given that y varies directly with x. y is 75 when x is 5. A. B. y = -15x C. y = 15x D. Lesson Quiz for Student Response Systems

12. Direct Variation 88 2. Identify the equation of direct variation given that y varies directly with x. x is 66 when y is 11. A. y = 66x B. y = 6x C. D. Lesson Quiz for Student Response Systems