Proportionality

  • Created by: Mxkuo_
  • Created on: 10-10-16 19:57

DIRECT PROPORTION

When 2 quantities are in direct proportion, as one increases so does the other or if one decreases so does the other

The general formula for this is:  y = kx

For example:

If y is directly proportional to x when x = 12 then y = 3. Find the constant of proportionality and the value of x when y = 8.

We know that y is proportional to x so y = kx

To find the value of k substitute the values y = 3 and x = 12 into y = kx

3 = k × 12

So k = 3/12 = 1/4

To find the value of x , when y = 8 substitute y = 8 and k = 1/4 into y = kx

8 = (1/4) x

So x = 32 when y = 8

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INVERSE PROPORTION

Inverse proportion is when one value increases as the other decreases

The general formula for this is:  y ∝ 1/x

For example;

y is inversely proportional to x. When y = 3, x = 12 .Find the constant of proportionality, and the value of x when y =8.

y ∝ 1/x so y = k/x

xy = k  so substitute the values x = 12 and y = 3 into xy = k

3 × 12 = 36

Sok = 36

To find the value of x when y = 8, substitute k = 36 and y = 8 into xy = k

x = 36/8 = 4.5

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PROPORTION AND GRAPHS

QUADRATIC :  y ∝ x2

image: graph (http://www.bbc.co.uk/staticarchive/230d558aabc2c837f275087bcc1a439b9b37cbb7.gif)

SQUARE ROOT:  y ∝square root of x (http://www.bbc.co.uk/staticarchive/ce9a80f41b711d96852b3d0aba4411343657860d.png)

image: graph (http://www.bbc.co.uk/staticarchive/7ceb701a943494a992f74c043310d479bee7d005.gif)

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PROPORTION AND GRAPHS (PT. 2)

INVERSE PROPORTION:   y ∝ 1/x 

Image result for y=1/x graph (http://www.coolmath.com/sites/cmat/files/page_images/precalculus-review-calculus-intro/precalculus-algebra/images/05-graphing-18.gif) 

  • Lines are asymptotes to the graph (they will never touch the axis)
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