Linear Equations What makes an equation a Linear

Linear Equations What makes an equation a Linear equation?

Definition Linear equations are functions which have two variables. They have independent and dependent variable.

Independent and Dependent Variables Independent variables are variables that can put into the equations. Dependent variables are variables that could solve.

introduction • If something is depending is independent, then it is on own. But if it is dependent, then it relies on someone or something else. • A dependent variable relies on what is used in place of the independent variable.

Y=m. X+b Y = 3 X - 2 Using the equation above, Y has to be the Dependent variable. Why? Because it is the variable that is being solved for.

Explanation Because linear equations have two variables, there are many possible combinations of answers. Those possible solutions are written as ordered pairs. Usually an ordered pair is written with the independent variable first then the dependent variable.

Example: y=5 x– 2 Because we solved for y, then x is the independent variable. The ordered pair would then be written as ( x , y ).

If we do not know which variable is independent, then we choose one. No matter which one is independent, we will still produce similar ordered pairs. ( w , z ) is similar to ( z , w )

x&y Most of the time when we use the variables x and y in an equation, x is independent and y is dependent.

Building a table To find more than solution, we use a Table of values there are many possible ordered pairs x y 3 13 -6 -28 0 -2 1 3

Practice • Examples to solve by students : § § y=x+7 2 a – 3 b = 5 3 r + s = 4 Z + 5 w = 11

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