Classifying Systems of Equations

Classify the lines below:

 $y=\frac{2}{5}x+\frac{9}{5}$  and  $y=\frac{-5}{2}x-3$  

• Parallel

• Perpendicular

• Neither

Classify the lines below:

 $y=2x+4$  and  $4y=8x+12$  

• Parallel

• Perpendicular

• Neither

 $Line\ a\ passes\ through\ \left(-2,\ -5\right)\ and\ \left(0,\ -1\right)$  

 $Line\ b\ passes\ through\ \left(3,\ 1\right)\ and\ \left(1,\ -3\right)\$  

Classify these lines

• Parallel

• Perpendicular

• Neither

 $Line\ a\ passes\ through\ \left(1,\ 4\right)\ and\ \left(3,\ 6\right)$  

 $Line\ b\ passes\ through\ \left(-3,\ -6\right)\ and\ \left(-1,\ -3\right)\$  

Classify these lines

• Parallel

• Perpendicular

• Neither

 $Line\ a\ passes\ through\ \left(-4,\ 5\right)\ and\ \left(-2,\ 8\right)$  

 $Line\ b\ passes\ through\ \left(-6,\ 7\right)\ and\ \left(-3,\ 5\right)\$  

Classify these lines

• Parallel

• Perpendicular

• Neither

 $y=3x+8\ \ and\ \ y=-3x\ +8$  

Determine the number of solutions

• one solution

• no solutions

• infinitely many solutions

 $y=\frac{4}{5}x-\frac{9}{5}\ \ and\ \ 4x-5y=9$  

Determine the number of solutions

• one solution

• no solutions

• infinitely many solutions

 $y=x-2\ \ and\ \ 7x-14y=-28$  

Determine the number of solutions

• one solution

• no solutions

• infinitely many solutions

 $y=2x+3\ \ and\ \ 2x-y=3$  

Determine the number of solutions

• one solution

• no solutions

• infinitely many solutions

 $y=6x-17\ \ and\ \ -12x+2y=-34$  

Determine the number of solutions

• one solution

• no solutions

• infinitely many solutions