1. Write linear equations that represent direct variation
Goal:
Write linear equations that represent direct variation
Eligible Content:
A / A

2. Vocabulary
Direct Variation - When two variables are related in such a way that the ratio of their values always remains the same.
y = kx
Constant of Variation – the relationship between the two variables k

3. In other words :
Direct variation is when one variable is a multiple of the other variable.
Equation looks like: y = kx
k can be any number except 0.
We call k the constant of variation.

4. Examples
Find the constant of variation and the slope of each direct variation problem. 1. y = 2x
2. y = - ½ x
m = - ½
k = - ½
m = 2
k = 2

5. Name the constant of variation for the equation
Name the constant of variation for the equation. Then find the slope of the line that passes through the pair of points.
A. constant of variation: 4; slope: –4
B. constant of variation: 4; slope: 4
C. constant of variation: –4; slope: –4
D. constant of variation: slope:

6. Name the constant of variation for the equation
Name the constant of variation for the equation. Then find the slope of the line that passes through the pair of points.
A. constant of variation: 3; slope: 3
B. constant of variation: slope:
C. constant of variation: 0; slope: 0
D. constant of variation: –3; slope: –3

7. Examples
The variables x and y vary directly. Use the given values to write an equation that relates x and y.
x = 5 and y = 20
x = -3 and y = -30
x = 10 and y = 5
x = 35 and y = 7
x = 17 and y = 4.25
y = 4x
y = 10x
y = ½ x
y = 1/5 x
y = ¼ x

8. Suppose y varies directly as x, and y = 15 when x = 5
Suppose y varies directly as x, and y = 15 when x = 5. Write a direct variation equation that relates x and y.
A. y = 3x
B. y = 15x
C. y = 5x
D. y = 45x

9. Practice
Worksheet – “3-4 Direct Variation”
Complete part A

10. More Examples
Assume the variables vary directly. Use an equation to find the value of y.
If x = 4 when y = 12, find y when x = -2.
If x = 1 when y = -7, find y when x = 3.
If x = 12 when y = 2, find y when x = 18.
If x = 3 when y = 36, find y when x = -4.
y = -6
y = -21
y = 3
y = -48

11. Suppose y varies directly as x, and y = 15 when x = 5
Suppose y varies directly as x, and y = 15 when x = 5. Use the direct variation equation to find x when y = –45.
A. –3
B. 9
C. –15
D. –5

12. More Practice
Worksheet – “3-4 Direct Variation”
Complete part B

13. Homework
Pages #10-15
#24-27