DS: Prep-1-16

[vantreal]

Lines n and p lie in the xy-plane. Is the slope of line n less than the slope of line p ?

(1) Lines n and p intersect at the point (5,1).

(2) The y-intercept of line n is greater than the y-intercept of line p.

Ans: (C)

but what I got is (E) :p

--------------------------------------------
my solution:
(1) an intersection point is not enough to determine, since
slope of line n and slope of line p might be:
+,+/+, -/ -, +/-,- -------------> insufficient

(2) the y-intercept of line n is greater than the y-intercept of line p.
again, slope of line n and slope of line p might be:
+,+/+, -/ -, +/-,- -------------> insufficient

(1) +(2),
consider the 4 possibilities
(slope of line n and slope of line p):
if +,+, then slope of line n < slope of line p
if +, -, then slope of line n > slope of line p
if -, +, then slope of line n < slope of line p
if -, -, then slope of line n > slope of line p

I am wondering whether my solution is flawed. :(

[vantreal]

ooops, i think i know where my mistakes are.

(1) +(2),
consider the 4 possibilities
(slope of line n and slope of line p):
if +,+, then slope of line n < slope of line p
if +, -, then slope of line n > slope of line p
if -, +, then slope of line n < slope of line p
if -, -, then slope of line n > slope of line p

here is the right solution:
if +, -, then it is highly impossible to have both lines intersect at (5,1)
if -, -, then slope of line n < slope of line p ---> sufficient

graphs do help :)

[Huang Hsin-Yi]

想問問看 上面正負是怎樣推的

[小花]

我也看不懂

但我解這題時 直接在紙上畫圖
兩條線交於 (5,1)
你會發現線與Y軸的焦點數值越大 斜率越小
畫畫看 很有趣的 故C

[Huang Hsin-Yi]

懂了