Linear EquationsLinear equations are functions whichhave two variables. They have anindependent and dependent variable.
Independent and DependentVariablesIndependent VariablesIndependent variablesare variables that youput into the equationsDependent VariablesDependent variablesare variables that yousolve for
Just as common sense would dictate. Ifsomething is independent, then it is on itsown. But if it is dependent, then it relies onsomeone or something else.A dependent variable relies on what is used inplace of the independent variable
y = 2x - 4Using the equation above, y has to be thevariableWhy? Because it is the variable that isbeing solved forDependent
Because linear equations have twovariables,there are many possiblecombinations of answersThose possible solutions are written asordered pairs. Usually an ordered pairis written with the independent variablefirst then the dependent variable
Example: y = 3x - 5Because we solved for y, then x isthe independent variableThe ordered pair would then bewritten as ( x , y )
If we do not know which variable isindependent, then we choose one. Nomatter which one is independent, we willstill produce similar ordered pairs( r , s ) is similar to ( s , r )Not congruent/equal
Most of the time when we use thevariables x & y in an equation, x isindependent and y is dependentThere are some exceptions, but we willwork with those at a much later time
As said before, there are many possibleordered pairsTo find more than one solution, we use aTable of Valuesx y2 3-2 10 -3
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