This week in math 10 we finished our polynomials unit and started our relations unit by reviewing what we learned in grade 9 on linear relations and relationships. I believe the most important thing I learned and reviewed this week was how relationships and variables work. This is important to me because as I start to use more complicated graphs and linear relations knowing and understanding the basics will help insure silly mistakes are not made.

 

Relationships and Variables:

The comparison between two sets of numbers is called a relation.

For example the liters of gas used is related to the distance the car travels.

In each relation there are two different variables that make up the relation.

The Independent Variable:

Input and variable X

The Dependent Variable:

Output and variable Y

 

There are five different ways relationships and variables are expressed.

The Table of Values

-In table of values the independent variable is located in the left column and the dependent variable is located in the right column.

Coordinates

-In coordinates the independent variable is located on the left side of the brackets and the dependent variable is located on the right side of the brackets.

Arrow Diagrams

-In arrow diagrams the independent variable is located in the left oval and the dependent variable is located in the right oval.

Equations

-In equations the independent variable is located on the right side of the equation and the dependent variable is located on the left side of the equation.

Graphs

-In graphs the independent variable is located on the horizontal line and the dependent variable is located on the vertical line.

A good tip to remember is that the independent variable is where you are starting from and the dependent variable depends on what the input value is.

 

Ex #1

A phones value, p, depends on its model, m.

-The independent variable is m and the dependent variable is p. The reason for this is because the value of the phone (the dependent variable) depends on the model (the independent model).

 

Ex #2

y=-x-5

-In this equation the independent variable is x and the dependent variable is y.