Question

Select the pair of equations whose graphs are perpendicular.    

A. 2y = –3x + 5    2x + 3y = 4

   

B. 5x – 8y = 9    12x – 5y = 7  

 C. y = 2x – 7     x + 2y = 3  

 D. x + 6y = 8     y = 2x – 8

Answer 1

`k:\ y=m_1x+b_1\ \ \ \ and\ \ \ \ l:\ y=m_2x+b_2\\ \\the\ line\k\ is\ perpendicular\ to\ the\ line\ l\ \ \ \Leftrightarrow\ \ \ m_1\cdot m_2=-1\\----------------------------\\\\A.\\2y=-3x+5\ \ \Rightarrow\ \ \ y=- (3)/(2) x+2.5\ \ \Rightarrow\ \ m_1=- (3)/(2) \\\\2x+3y=4\ \ \Rightarrow\ \ 3y=-2x+4\ \ \Rightarrow\ \ y=- (2)/(3)x+1 (1)/(3) \ \ \Rightarrow\ \ m_2=- (2)/(3) \\\\m_1\cdot m_2=- (3)/(2) \cdot (- (2)/(3))=1 \\eq -1`


`B.\\5x-8y=9\ \ \Rightarrow\ \ -8y=-5x+9\ \ \Rightarrow\ \ \ y= (5)/(8) x-1 (1)/(8) \ \Rightarrow\ \ m_1= (5)/(8) \\\\12x-5y=7\ \Rightarrow\ \ -5y=-12x+7\ \ \Rightarrow\ \ y= (12)/(5)x-1 (2)/(5) \ \ \Rightarrow\ \ m_2= (12)/(5) \\\\m_1\cdot m_2= (5)/(8) \cdot (12)/(5)= (3)/(2) \\eq -1`


`C.\\y=2x-7\ \ \Rightarrow\ \ m_1=2 \\\\x+2y=3\ \Rightarrow\ \ 2y=-x+3\ \ \Rightarrow\ \ y= -(1)/(2)x+1 (1)/(2)\ \ \Rightarrow\ \ m_2=- (1)/(2) \\\\m_1\cdot m_2= 2 \cdot (- (1)/(2))= -1\ \ \Rightarrow\ \ y=2x-7\ \ \ \ \perp\ \ \ \ x+2y=3`


`D.\\x+6y=8\ \ \Rightarrow\ \ 6y=-x+8\ \ \Rightarrow\ \ \ y=- (1)/(6) x+1 (1)/(3)\ \ \Rightarrow\ \ m_1= -(1)/(6) \\\\y=2x-8\ \Rightarrow\ \ m_2= 2 \\\\m_1\cdot m_2= -(1)/(6) \cdot2=- (1)/(3) \\eq -1`