Question

In the rectangular coordinates，abscissa and ordinate of the intersection point of the lines y=x-k and y=kx+2 are integers for imteger k，then the number of the possible values of k is
（英漢小詞典：abscissa橫坐標(biāo)；ordinate縱坐標(biāo)；intersectionpoint交點(diǎn)；integer整數(shù)）

1. A.
   4
2. B.
   5
3. C.
   6
4. D.
   7

Answer 1

A
分析：讓直線y=x-k，y=kx+2組成方程組，消去y，根據(jù)x，k均為整數(shù)求得k可能的整數(shù)解的個(gè)數(shù)即可．
解答：，
x-k=kx+2，
（x+1）k=x-2，
k=1+，
∵x+1可取±1，±3共4個(gè)數(shù)，
∴相對(duì)應(yīng)的k的值也要有4個(gè)．
故選A．
點(diǎn)評(píng)：本題考查了直線的相交問(wèn)題；組成方程組消去一個(gè)未知數(shù)是解決本題的突破點(diǎn)；找相應(yīng)的整數(shù)解是解決本題的難點(diǎn)．