Direct Variation
January 3, 2012
SWBAT: Identify, write, and graph direct variation.
1 3
2 6
6–3
2–1
r = 11
=
3
1
m = 3
SWBAT: Identify, write, and graph direct variation.
SWBAT: Identify, write, and graph direct variation.
SWBAT: Identify, write, and graph direct variation.
Identifying Direct Variations from Equations
1)Tell whether the equation represents a direct
variation. If so, identify the constant of variation.
1) y = 21x
This equation represents a direct variation
because it is in the form of y = kx. The
constant of variation is 21.
YES!
k = 21
SWBAT: Identify, write, and graph direct variation.
Identifying Direct Variations from Equations
2) Tell whether the equation represents a direct
variation. If so, identify the constant of variation.
2) 3x + y = 8
3x + y = 8
–3x
–3x
y = –3x + 8
Solve the equation for y.
This equation is not a direct variation because it
cannot be written in the form y = kx.
NO!
SWBAT: Identify, write, and graph direct variation.
Identifying Direct Variations from Equations
3) Tell whether the equation represents a direct
variation. If so, identify the constant of variation.
–4x + 3y = 0
+4x
+4x
3y = 4x
Solve the equation for y.
This equation represents a
direct variation because it is
in the form of y = kx.
Yes!
SWBAT: Identify, write, and graph direct variation.
Identifying Direct Variations from Equations
4) Tell whether the equation represents a direct
variation. If so, identify the constant of variation.
3x + 0 = 15y
Solve the equation for y.
3x = 15y
15
15
This equation represents a
direct variation because it is
in the form of y = kx.
Yes!
SWBAT: Identify, write, and graph direct variation.
What happens if you solve y = kx for k?
y = kx
Solve the equation for k.
So, in a direct variation, the ratio is equal to the
constant of variation. Another way to identify a
direct variation is to check whether
is the same
for each ordered pair (except where x = 0).
SWBAT: Identify, write, and graph direct variation.
5) Tell whether the relationship is a direct variation.
Explain.
Method: Find
for each ordered pair.
YES!
K = 3
SWBAT: Identify, write, and graph direct variation.
6) Tell whether the relationship is a direct variation.
Explain.
Method: Find
for each ordered pair.
…
NO!
SWBAT: Identify, write, and graph direct variation.
Does not pass
thru the
origin.
NO!
-9
7
Yes!
SWBAT: Identify, write, and graph direct variation.
9) The value of y varies directly with x, and y = 3
when x = 9. Find y when x = 21.
Method : Use a proportion.
In a direct variation is the same for all
values of x and y.
9y = 63
y=7
Use cross products.
Since y is multiplied by 9 divide both
sides by 9.
SWBAT: Identify, write, and graph direct variation.
10) The value of y varies directly with x, and
y = 4.5 when x = 0.5. Find y when x = 10.
Method : Use a proportion.
In a direct variation is the same for all
values of x and y.
0.5y = 45
y = 90
Use cross products.
Since y is multiplied by 0.5 divide both
sides by 0.5.
SWBAT: Identify, write, and graph direct variation.
SWBAT: Identify, write, and graph direct variation.