请教gwd-23-27: 为澄清一个概念

jennifer1985

Q27:

If line k in the xy-plane has equation y = mx + b, where m and b are constants, what is the slope of k ?

(1)     k is parallel to the line with equation y = (1 – m)x + b + 1.

(2)     k intersects the line with equation y = 2x + 3 at the point (2, 7).

答案是A,但我认为应该是D.条件(1) 推出 m=1-m, 所以m=1/2

条件(2) point (2, 7)带入y = mx + b, 推出7=2m+b. 因为题目给出条件 m and b are constants, 推出7=2m+(m+1)或7=2m+(m-1), 最后得出m=2或m=8/3.  但我认为 m and b are constants, 应该是涉及整数才说 constants的. 所以m=2.

大家如何看?

detectiveyan

How did you get 7=2m+(m+1)? The only conclusions you can get from (2) alone should be:

1. the slop of line k doesn't equal to 2, otherwise k will be parallel to the line y=2x+3.

2. (2, 7) is on line k, so 7=2m+b.

Neither of these two conclusions will give you m.

Also,when given "m and b are constants"  that only means this equation of line k is a 一元一次方程.

yuguanglais

 constants是常数的意思，做形容词的时候才是连续的意思．

关于（２）你想象一条直线与另外一条交在一个点上，是可以在这个点３６０旋转的哦，那斜率怎么可能一定呢

jennifer1985

Thanks for both of your girls' clarification!

Yes, I wrongly regard "constant" as 连续整数! What a mistake!!

Economics

知道一点，是没有办法求出一条直线的斜率啊，所以应该是选A.

tomatohuas

选A?