Linear Equations in Standard Form

Linear Equations in Standard Form

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Red flags indicating that equation is NonLinear

• Division by the variable (on on the bottom)

• Radicals or square root

• Exponent other than 1

• Multiplication of two variables

Multiple Select

Which equations are Linear?

• $y\ =\ 3x\ +\ 9$

• $y\ =\ \frac{3}{x}$
  

• $y\ =\ 9$
  

• 
  

  $y=x^2+5$

Standard Form of Linear Equations

Open Ended

Is the following equation in a Standard Form? 

If yes - write yes
If not - explain why
 $2x\ +4y\ =\ 7$  

Open Ended

Is the following equation in a Standard Form? 

If yes - write yes
If not - explain why
 $-2x\ +4y\ =\ 7$  

Open Ended

Is the following equation in a Standard Form? 

If yes - write yes
If not - explain why
 $2x\ \ -\ 4y\ =\ 7.8$  

Open Ended

Is the following equation in a Standard Form? 

If yes - write yes
If not - explain why
 $2x\ \ =\ 7$  

Identify A, B, and C

Multiple Choice

Identify A,B, and C

 $x+3y\ =\ -6$  

• A = 0, B = 3, C = -6

• A=1, B = 3, C = -6

• A = 3, B = -1, C = -6

• Cannot be determined

Multiple Choice

Identify A,B, and C

 $3y\ =\ -6$  

• A = 0, B = 3, C = -6

• A=1, B = 3, C = -6

• A = 3, B = 0, C = -6

• Cannot be determined

Multiple Choice

Identify A,B, and C

 $x\ =\ -6$  

• A = 0, B = 1, C = -6

• A=1, B = 1, C = -6

• A = 1, B = 0, C = -6

• Cannot be determined

Multiple Choice

Identify A,B, and C

 $2x+3y\ =\ 15$  

• A = 3, B = 2, C = 15

• A=2, B = 3, C = 15

• A = 15, B = 2, C = 3

• Cannot be determined

Writing an equation in Standard form

• Determine if equation is Linear

• Put x and y terms on the left side - do not forget to change the sign

• If A is negative - multiply by (-1) all the terms

• If there are fractions - multiply by the denominator all the terms

Open Ended

Write an equation in standard form

 $2x\ =\ 3y-5$  

Open Ended

Write an equation in standard form

 $x\ =\ \frac{4}{5}y-7$  

Open Ended

Write an equation in standard form

 $-2x\ =\ 4y$  

Open Ended

Write an equation in standard form

 $-5y\ =\ 4x\ +\ 2$  

Open Ended

Write an equation in standard form

 $3x\ +2=\ 4y\$