Direct vs. Inverse Variation

1
Direct vs. Inverse Variation
2
Direct Variation
As one variable increases, the other must also
increase ( up, up) OR As one variable decreases,
the other variable must also decrease. (down,
down)
3
Real life?

• With a shoulder partner take a few minutes to
  brainstorm real life examples of direct
  variation. Write them down.

Food intake/weight Exercise/weight loss Study
time/ grades
4
Direct Variation

• y kx
• k is the constant of variation
• the graph must go through the origin (0,0) and
  must be linear!!

5
Direct Variation
Ex 1)If y varies directly as x and y 12
when x 3, find y when x 10.
2 ways to solve.
6
What did we do?
Use ykx
EITHER ONE WILL WORK!! ITS YOUR CHOICE!
7
Direct Variation Application

• Ex 2) In scuba diving the time (t) it takes a
  diver to ascend safely to the surface varies
  directly with the depth (d) of the dive. It
  takes a minimum of 3 minutes from a safe ascent
  from 12 feet. Write an equation that relates
  depth (d) and time (t). Then determine the
  minimum time for a safe ascent from 1000 feet?

8
Inverse Variation
As one variable increases, the other decreases.
(or vice versa)
9
Inverse Variation

• This is a
• NON-LINEAR function (it doesnt look like
  ymxb)
• It doesnt even get close to (0, 0)
• k is still the constant of variation

10
Real life?

• With a shoulder partner take a few minutes to
  brainstorm real life examples of inverse
  variation. Write them down.

Driving speed and time Driving speed and gallons
of gas in tank
11
Inverse Variation
Ex 3) Find y when x 15, if y varies inversely
as x and when y 12, x 10.
2 ways to solve
12
What did we do?
EITHER ONE WILL WORK!! ITS YOUR CHOICE!
13
Inverse Variation Application
Ex 4)The intensity of a light I received from a
source varies inversely with the distance d
from the source. If the light intensity is 10
ft-candles at 21 feet, what is the light
intensity at 12 feet? Write your equation first.
14
REFLECTION

• With a shoulder partner, use the LEFT side in
  your notebook and create a Double Bubble Map to
  compare/contrast Inverse and Direct Variation

Hmmwhat did I learn?
15
Direct vs. Inverse Variation