Question

Find the distance between the pair of parallel lines, y = -2x+1 & y = -2x+16.

Answer 1

`Given \ the \ equations \ of \ two \ non-vertical \ parallel \ lines:\\\\y = mx+b_1\\y = mx+b_2\\\\the \ distance \ between \ them \ can \ be \ expressed \ as : \\\\d= (|b_(1)-b_(2)|)/( √( m^2+1) )`


`y = -2x+1\\y = -2x+16 \\\\\\d= (|b_(1)-b_(2)|)/( √( m^2+1) ) =(| 1-16|)/( √( (-2)^2+1) ) =(| -15|)/( √( 4+1) ) =(15)/(√(5))\cdot (√(5))/(√(5))=\\ \\\\=(15√(5))/(5)=3√(5)\approx 3\cdot 2.24 \approx 6.72`