February 28, 2017
`
5.2 Direct Variation
Objectives:
To determine if an equation or situation represents direct variation
To write and graph direct variation equations
Bellwork: Discuss the two graph below and their characteristics. How are they alike? How are they different?
Could you write an equation for each?
February 28, 2017
5.2 Direct Variation
Objectives:
To determine if an equation or situation represents direct variation
To write and graph direct variation equations
1. This shower head allows 5 gallons of water per minute...
If y gallons of water are used during an x minute shower, what equation would represent the situation?
How much water would be used during a shower of 3 minutes?
February 28, 2017
Both of these examples represent a direct variation equation...
Direct Variation­shows a relationship that can be represented by the function y = kx (where k 0)
k = constant of variation
is another way to write the equation.
Graph: Both linear
Both go through
the origin Does the equation represent direct variation? If so, what is the constant of variation?
5. 5y = x
1. y = 6x
2. y = 4x ­ 1
6. 5y ­ 15x = 0
3. c = 1/2x
4. 3y = 6x
7. 3y + 6 = 9x
8. ­9 + 2x + 9 = 4y
February 28, 2017
p. 304 (9‐14)
February 28, 2017
Writing Direct Variation Equation
y varies directly with x. write direct variation equation
A. Write a direct variation equation that relates x and y. plug in the values
they give you
B. Then, find the value of y if x = 8. Use original equation written to plug in the x value. 9. x = 4, y = 12
Solve for k
10. x = 15, y = 3
Find y when x = 8.