Finding the rule in a relation - Mr. Azouz' s Math Class



Finding the rule in a relation

We know that a relation is two things related with two variables

The Independent variable x

The Dependent variable y

We also know how to find both variable since

Y (Dep. Var) always depends on X (Ind. Var)

Note: x usually time

y usually money

In every relation, there is rule.

The rule is a mathematical equation that can tell us everything we need to know about that relation. A general form of the rule is:

Y = dependent variable (what happens second?)

a = rate of change (how much does it change by?)

X = Independent variable (what happens first?)

b = initial value (how much does the relation start with?)

EXAMPLE:

Kyle works as plumber. He gets 10 dollars an hour but also gets 50 dollars for showing up for work. What is the relation that describes this situation?

What is the independent variable? x = hours worked

What is the dependent variable? y = money earned

What is the Rate of change? a = 10 dollars every hour

What is the Initial value? b = 50 dollars to start with

What is the Rule for this relation? y = 10x + 50

Draw a table of values

The next step would be to create a table of values where using the rule you can fill in the table

|X = Hours |Y = |

| |$ |

|0 |50 |

|1 |60 |

|2 |70 |

|3 |80 |

|4 |90 |

|5 |100 |

|10 |150 |

Graph:

When making the graph, remember:

← Labels

← Scale

← Use the numbers from table of values

200 | | | | | | | | | | |180 | | | | | | | | | | |160 | | | | | | | | | | |140 | | | | | | | | | | |120 | | | | | | | | | | |100 | | | | | | | | | | |80 | | | | | | | | | | |60 | | | | | | | | | | |40 | | | | | | | | | | |20 | | | | | | | | | | |0 |1 |2 |3 |4 |5 |6 |7 |8 |9 | |

-----------------------

Hours X

$ Y

When x = 0

means no hours Kyle makes 50 $

Or y = 10 (0) +50

Y = 0 +50

Y = 50$

When x = 1

means 1 hour Kyle makes 50 $ + 10$

Or y = 10 (1) +50

Y = 10 +50

Y = 60 $

Y = ax + b

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