1. Direct and Inverse Variation
Day 2

2. General Equation
The general equation for direct variation is
k is called the constant of variation.

3. Example
If y varies directly as x, and y=24 and x=3 find the constant of variation.

4. Example
y varies directly as x, and x=8 when y=9. Find the constant of variation.
y = kx
9 = 8k
k = 9/8

5. Example y varies directly as x, and x=8 when y=9. Find y when x = 4.
Use the formula for direct variation.
Y = 4.5

6. Inverse Variation y varies inversely as x if such that xy=k or
Just as with direct variation, a proportion can be set up solve problems of indirect variation.

7. Indirect Variation
Lets do an example that can be solved by using the equation and the proportion.

8. Solve:
Find x when y=27, if y varies inversely as x and x=9 when y=45.
Answer: 15

9. Determine if the chart is a direct variationx 10 12 14 16 18 y 20 24 28 32 36
To solve, find the constant of variation for each pairing of numbers using the formula y=kx.
YES! The constant of variation is 2.

10. Determine if the chart is a direct variationx 20 16 12 8 4 y 10 6 2
To solve, find the constant of variation for each pairing of numbers using the formula y=kx.
YES! The constant of variation is 1/2.

11. Determine if the chart is a direct variationx 6 9 15 18 24 y 2 3 5 12
To solve, find the constant of variation for each pairing of numbers using the formula y=kx.
NO! The constant of variation is changes and is not the same for all pairs.

12. Determine if the charts are direct variationsx 2 8 9 14 18 y 6 24 27 42 54 x -3 9 15 18
-21 y -2 6 10 12
-14 x -1 3 5 8 10 y -2 6 12
-14