Question

Determine the given pair of lines of parallel, perpendicular, or intersecting.

1. Y=7/3x _8 and Y=7/3 x + 3
2. Y=2x _ 1 and _x + 2y=6
3. Y= 5/2 x_17 and Y= _5/2x _1
4. Y=5/2x_4 and _5x + 2y=6
5. Y=_2/3x +12 and Y=3/2x +3
6. Y=1/3x _13 and Y= 3x + 2
7. Y=_4x + 5 and _x + 4y =_16
8.Y=2/3x + 3 and _2x + 3y =21

Answer 1

`k:\ y=m_1\cdot x+b_1\ \ \ \ and\ \ \ \ l:\ y=m_2\cdot x+b_2 \\\\k\ ||\ l\ \ \ \Leftrightarrow\ \ \ m_1=m_2\ \ \ \ \ \ and \ \ \ \ \ \ k\ \bot\ l\ \ \ \Leftrightarrow\ \ \ \ m_1\cdot m_2=-1\\----------------------------\\1.\\ k:\ y= (7)/(3) x-8\ \ \ and\ \ \ l:\ y=(7)/(3) x+3\\\\m_1=m_2=(7)/(3)\ \ \ \Rightarrow\ \ \ k\ ||\ l`


`2.\\k:\ y=2x-1\ \ and\ \ l:\ -x+2y=6\ \Rightarrow\ \ 2y=x+6\ \ \Rightarrow\ \ y= (1)/(2)x+3 \\\\m_1 \\eq m_2\ \ \ and\ \ \ m_1\cdot m_2 \\eq -1\ \ \ \Rightarrow\ \ \ the\ lines\ intersect\\\\3.\\k:\ y= (5)/(2) x-17\ \ \ and\ \ \ l:\ y=- (5)/(2) x-1\ \ \ \Rightarrow\ \ \ the\ lines\ intersect\\\\4.\\k:\ y= (5)/(2) x-4\ \ and\ \ l:\ -5x+2y=6\ \Rightarrow \ 2y=5x+6\ \Rightarrow \ y= (5)/(2)x +3\\\\m_1=m_2= (5)/(2) \ \ \ \Rightarrow\ \ \ k\ ||\ l`


`5.\\k:\ y=- (2)/(3) x+12\ \ \ and\ \ l:\ y= (3)/(2) x+3\\\\m_1\cdot m_2=- (2)/(3)\cdot (3)/(2) =-1\ \ \ \Rightarrow\ \ \ k\ ||\ l\\\\6.\\k:\ y= (1)/(3)x-13\ \ \ and\ \ \ l:\ y=3x+2\ \ \ \Rightarrow\ \ \ the\ lines\ intersect \\\\7.\\k:\ y=-4x+5\ \ ,\ \ l: -x+4y=-16\ \Rightarrow\ 4y=x-16\ \Rightarrow\ y= (1)/(4)x-4 \\\\m_1\cdot m_2=-4\cdot (1)/(4) =-1\ \ \ \Rightarrow\ \ \ k\ \bot\ l`


`8.\\k:\ y= (2)/(3) x+3 \ ,\ \ l:\ -2x+3y=21 \ \Rightarrow\ \ 3y=2x+21\ \Rightarrow\ y= (2)/(3) x+7\\\\m_1=m_2= (2)/(3) \ \ \ \Rightarrow\ \ \ k\ ||\ l`