Additive Relationship  y = x + a

In an additive relationship, two quantities can be expressed as related to each other through addition.

It can be written as y = x + a, where y is related to x through the addition of a constant, “a”.  The value for a may be positive or negative.

Example: firefighters use special clothing and equipment called “turnout gear.” The extra weight is approximately 60 pounds.  What is the total weight of both the firefighter and his equipment in pounds?

Situation: Total weight will always be 60 pounds more than the firefighter weight without equipment

This table shows an additive relationship between x and y, represented with           y = x + 60

 

 

 

 

 

 

From the table, we place points in a coordinate plane using the ordered pairs (x,y)}

 

y = x + 60

 

 

 

 

 

 

In an additive relationship,

y = x+a

The set of points will lie in a linear pattern and will not contain the ordered pair (0,0)

More examples of Additive Relationships:

 

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Multiplicative Relationship   y = ax

A multiplicative relationship is a relationship where two quantities can be expressed as multiples of each other. Its equation is y = ax,  where “a” is  to the ratio of y to x.

 

Example Gallons to quarts’ conversion

 

 

 

The multiplicative relationship, y = 4x, is represented graphically by placing points in the coordinate plane where the independent variable is the x-value and the dependent variable is the y-value.

 

 

 

 

 

 

 

The set of points will lie in a linear pattern and will contain the ordered pair (0,0)