Transcript Direct and Inverse Variations

Direct and Inverse
Variations
section 9-2
Direct Variation
when
we talk about a
direct variation, we are
talking about a relationship
where as x increases, y
increases or decreases at a
CONSTANT RATE.
Direct Variation
the
gist of direct variation
is the following formula:
y1 y 2

x1 x 2
Direct Variation
example:
if
y varies directly as x and
y = 10 as x = 2.4, find x
when y =15.
what x and y go together?
Direct Variation
if
y varies directly as x and y =
10 as x = 2.4, find x when y =15
y
= 10, x = 2.4 => make
these y1 and x1
y = 15, and x = ? => make
these y2 and x2
Direct Variation
if
y varies directly as x and y =
10 as x = 2.4, find x when y =15
10 15

2.4 x
Direct Variation
How
do we solve this? Cross
multiply and set equal.
10 15

2.4 x
Direct Variation
We
get: 10x = 36
Solve for x by diving both
sides by 10.
We get x = 3.6
Direct Variation
Let’s
do another.
If y varies directly with x
and y = 12 when x = 2, find
y when x = 8.
Set up your equation.
Direct Variation
If
y varies directly with x and
y = 12 when x = 2, find y
when x = 8.
12 y

2 8
Direct Variation
Cross
multiply: 96 = 2y
Solve for y.
48 = y.
Direct Variation
From
the 9-2 Study Guide,
complete problems 2, 4, &
7.
Direct Variation
#2
6y
y 9

8 6
= 72
y = 12
Direct Variation
#4
9 5

x 15
135
= 5x
x = 27
Direct Variation
#7
1000 50

x
200
200,000 = 50x

x
= 4000
Inverse Variation
Inverse
is very similar to
direct, but in an inverse
relationship as one value
goes up, the other goes
down. There is not
necessarily a constant rate.
Inverse Variation
With
Direct variation we
Divide our x’s and y’s.
In Inverse variation we
will Multiply them.
 x 1 y1
= x2y2
Inverse Variation
If
y varies inversely with x and
y = 12 when x = 2, find y when
x = 8.
 x 1 y1
= x2y2
2(12) = 8y
24 = 8y
y=3
Inverse Variation
If
y varies inversely as x
and x = 18 when y = 6, find
y when x = 8.
18(6)
= 8y
108 = 8y
y = 13.5
Inverse Variation
Try
some on your own.
On your worksheet:
# 1, 6, 8
Inverse Variation
#1
15(y)
= 10(12)
15y = 120
y = 8
Inverse Variation
#6
27(x)
= 9(45)
27x = 405
x = 15
Inverse Variation
#8
76(y)
= 38(100)
76y = 3800
y = 50
Direct & Inverse
Variation
Assignment
1-8
- wkst 9-2