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When two quantities are related proportionally, the ratio of one quantity to the other is invariant as the numerical values of both quantities change by the same factor.
-proportional quantities maintain a constant ratio.

Ex: 5x + 4 = 24
5x=20
x=4

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One quantity increases while another quantity decreases and the product of quantities remains constant.
-the graph is curve with no x-intercept or y-intercept
y=k/x  or  xy=k

Ex: you have $200 to invest. Assume that there are no fees and that you will spend all the money with a purchase of stocks in one company. Let x be the number of stocks you can purchase and let y be the cost per stock.
xy= 200
or
y= 200/x

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One quantity is directly proportional to another when the ratio of the two quantities is constant.
-When y changes, x changes

Ex: A girl works 24 hours per week and makes $320 before taxes.

y=13.3x

x- number of hours she works
y- amount of money paid

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Compare how much of something per one.

x: 50 miles per hour

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Alters the original amount by quantity relative to the original amount.
Ex:
Describing a change from 4 to 12 as multiplying by 3.

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A ratio comparing one part to the whole.

Ex:

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Alters the original amount by an absolute.

Ex:
Describing a change from 4 to 12 as addition 8.

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A ratio comparing one part to another.

EX:

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-is a number that relates two quantities or measures within a given situation in a multiplicative relationship.
-A comparison or a relationship between two quantities.

Ex: A ratio of 5 red squares to 3 green squares.
-5:3
-5 to 3
-5 red squares/3 green squares

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Two quantities can be expressed as related to each other through addition. Can be written as y= x + a

Ex: y= x + 5

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Two quantities that can be expressed as multiples of each other. Can be written as y= a x

Ex: A theater charges $15 admission for every person.
y= 15x
x: number of people

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Understanding that every quantity we measure is relative to another pre-measured group, a unit.

Ex: three groups of two smiley faces.

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The property of a function of retaining its form when the variables are linearly transformed.