Line L goes through (a,b), (c,d). Is the slope of line L

Question

Line L goes through (a,b), (c,d). Is the slope of line L negative?

1) The product of intersect L with X and intersect L with Y is positive; 

2) (a-b)(c-d)<0

Dookie · Answer

Could you please explain statement 2 ?

ian7777 · Answer

sure. remember what slope is. it's y-y/x-x. In this case the slope of this line would be :beat

wait a minute. I just reread this and I misread it originally. I thought the second statment was saying that (a-c)(b-d)<0, but it's not. It says (a-b)(c-d)<0. The first way is how I originally saw this problem (when I saw it from a different source) and in that case the answer's d. As it's written here I think it wouldn't work. Answer A.

twixt · Answer

Statement 1 is crystal clear.

I spent a couple of minutes on second statement but I didnt find out what it is supposed to hide...

pjk · Answer

st 2: (a-b)(c-d)<0 Case 1: ad (a,b)= (1,5) (c,d)= (5,1) => -ve slope (a,b)= (1,5) (c,d)= (-1,-5) => +ve slope Hence not B. Didnt bother to check other case. Case 2: a>b and c

nocilis · Answer

1) If the product of x and y intercepts are positive, the intercepts have to be both -ve. So the line has negative slope

2) Slope - y2-y1/x2-x1 = (d-b)/(c-a)
Here they have given that an unrelated product (a-b)*(c-d) <0.
So, can get an answer from this. Perhaps substituting some values might also help.

A it is.

Sargataur · Answer

Q for nocilis

why cant the intercepts be positive for thier product to be positive...why r u just consdiering intecepts negative case...

nocilis · Answer

I meant:
 If the product of x and y intercepts are positive, the intercepts have to be both -ve  or both positive . In both cases the slope is negative

For a line intersecting on both x and y axis with Positive Slope:
The following are possible:
X intercept +ve, Y intercept -ve
X intercept -ve, Y intercept +ve

Line is going this way: '/'

For a line intersecting on both x and y axis with Negative Slope:
The following are possible:
X intercept +ve, Y intercept +ve
X intercept -ve, Y intercept -ve

Line is going this way: '\'

Line L goes through (a,b), (c,d). Is the slope of line L

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