Question

Which pair of equations represents perpendicular lines?

a. {y=1/2x+2 {y=-1/2x+4
b. {y=5x+7 {y=-1/5x+3
c. {y=1/5x+2 {y=1/5x+1
d. {y=3x+4 {6x+8

Answer 1

`The\ slope-intercept\ form:y=mx+b\\\\k:y=m_1x+b_1\ and\ l:y=m_2x+b_2\\\\k\perp l\iff m_1\cdot m_2=-1\Rightarrow m_2=-(1)/(m_1)\\-----------------------\\therefore\\a)\ m_1=(1)/(2);\ m_2=-(1)/(2)\ \boxed{NOT\ :(}\\\\b)\ m_1=5;\ m_2=-(1)/(5)\ \boxed{YES\ :)}\ \ 5\cdot(-(1)/(5))=-1\\\\c)\ m_1=(1)/(5);\ m_2=(1)/(5)\ \boxed{NOT\ :(}\\\\d)\ m_1=3;\ m_2=6\ \boxed{NOT\ :(}`