Transcript Lesson 6-9: Variation

Lesson 6-9: Variation
Objective:
Students will:
oFind the constant of variation and setup direct and
oUse variation equations to solve problems
inverse variation equations
Direct Variation
Equations:
y
k
x
or
y  kx
Why direct?
Take
16
or
2
8
16  2  8
, where k = 2
If y goes up, x must go up
y and x move the same → direct
“k” is the constant of variation – must stay constant
Inverse Variation
Equations: x  y  k
or
k
y
x
Inverse → opposite → if y goes up, x must go down…
Choosing
Identify the variables
Ask: if the one value increases, what will the other do?
increase also → direct
decrease → inverse
Example 1
The force applied to a spring causes the length to increase. 8
pounds makes the spring 4 inches. Find k and write a general
equation.
Which type of variation?
Direct
What would be the x variable? y?
x: pounds y: inches
y
k
x
4
k
8
1
k
2
1
y x
2
What would be the length if the weight is 20lbs?
1
y  (20)  10in
2
Example 2
Time (t) required to do a job varies inversely with the number of
people working. It takes 4hrs for 12 people to put up
bleachers. Write the equation to represent the problem.
x y  k
48
y
x
12  4  k
48  k
How long would it take 3 people to do the same job.
48
y
3
y  16hrs
Marker Board pg 283-284
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Assignment/6-9/283-284/3-27M3,34-42e