MathDB

On the coordinate plane, is there a line family of infinitely many lines

l_1,l_2,\cdots,l_n,\cdots

, satisfying the following? (1) Point

(1,1)\in l_n

for all

n\in \mathbb{Z}_{+}

. (2) For all

n\in \mathbb{Z}_{+}

k_{n+1}=a_n-b_n

, where

k_{n+1}

is the slope of

l_{n+1}

a_n,b_n

are intercepts of

l_n

x

-axis,

y

-axis. (3)

k_nk_{n+1}\geq0

for all

n\in \mathbb{Z}_{+}

Problem Statement