Indirect Worksheets - PowerPoint

							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
ify 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
ify 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
Fromthe 9-2 Study Guide,
complete problems 2, 4, &
7.
      Direct Variation
#2
       y 9
        
       8 6
6y = 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.
x1y1   = x2y2
      Inverse Variation
If y varies inversely with x and
 y = 12 when x = 2, find y when
 x = 8.
x1y1 = x2y2
2(12) = 8y
24 = 8y               y=3
      Inverse Variation
Ify 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   - wkst 9-2
1-8