Question

Find the slope of a line perpendicular to each given line

Answer 1

`k:\ y=m_1x+b_1\\l:\ y=m_2x+b_2\\\\l\ \perp\ k\iff m_1m_2=-1\to m_2=-(1)/(m_1)`

`115)\ -x-y=3\ \ \ |+x\\-y=x+3\ \ \ |\cdot(_1)\\y=-x-3\to m_1=-1\to\boxed{m_2=-(1)/(-1)=1}\\\\116)\ 0=-4x-y+5\ \ \ |+y\\y=-4x+5\to m_1=-4\to\boxed{m_2=-(1)/(-4)=(1)/(4)}\\\\117)\ 6-2y=x\ \ \ \ |-6\\-2y=x-6\ \ \ \ |:(-2)\\y=-(1)/(2)x+3\to m_1=-(1)/(2)\to\boxed{m_2=-(1)/(-(1)/(2))=2}\\\\118)\ 5y=25+4x\ \ \ \ |:5\\y=5+(4)/(5)x\to m_1=(4)/(5)\to\boxed{m_2=-(1)/((4)/(5))=-(5)/(4)}`

`119)\ -15x-9y=9\ \ \ \ |+15x\\-9y=15x+9\ \ \ \ |:(-9)\\y=-(15)/(9)x-1\\y=-(5)/(3)x-1\to m_1=-(5)/(3)\to\boxed{m_2=-(1)/(-(5)/(3))=(3)/(5)}`