Line L passes through point (1,4) and the product of its

Question

Line L passes through point (1,4) and the product of its intercepts with axis x and axis y is negative. Which of the following point is on the line L?

A. (2,3)
B. (5,7)
C. (4,2)
D. (4, -1)
E. (5, -1)

I got confused and selected E.

Professor · Answer

wow, good one.... B . (5, 7)

ipc302 · Answer

Is the answer B .?? (5,7)

 i used different approach so not sure of the answer

say the intercept of x axis be a 
 the intercept of y axia be b 

 so x/a + y/b =1

slope = -b/a --- equation 1 

but given a * b = -1

 so a = -1/b substitute this value in equation 1 

 u get slope = b^2 which mean slope will always be positive 

now from the point (1,4 ) find the slope with each of the no given and only 
option B (5,7) has a positive slope rest of them gives -ive slope .

Do let me know the answer , as i've mentioned above i never solved using the above way , just wanted to solve it fast and thought of the above way .i didnt want to solve it in 10 min but just around 2 min .I'm curious to know the answer . Thanks.

kuristar · Answer

Sorry to be the 'dumb blonde' but could you explain?

Thank you!

kuristar · Answer

You are right, the oa is (5,7).

Now I have to try to get it right!

remgeo · Answer

I dont see why I did that, but still I took the slope for each of the cases, 

ie. (y2 - y1)/ (x2 - x1)

For all except B, I got a negative slope. 

Since B was the only different one, I selected B. 

But can someone please explain why the slope has to be positive?

ipc302 · Answer

remgeo,

 if you see my post above i have derived why slope has to be positive .

 the slope has to be B^2 and obviously that will always be positive .

Thanks.

x242222 · Answer

I selected B. 

I just drew out an xy graph and put a dot on (1,4). From there, I knew that the product of the x intercept and y intercept needed to be negative.

So I went down through the answer choices and looked for a line that crossed either the x or the y axis at a negative point. 

(A) Doesn't work because when you draw the line, the x and y intercepts are both positive. Hence when you multiple them, the number will be positive. If you want to solve it out, the x intercept here would be (5,0). The y intercept would be (0,5). When you multiply, the ans is positive. 
(B) When you plot this point and draw a line that goes through (1,4), you will see a negative slope. The y intercept is positive, but if you keep tracing the line, it crosses the x axis at a negative point. When you multiply the two products, the number will be negative. B is correct.
(C) Same situation as A
(D) Same situation as A. Despite the negative number, the x intercept is still positive.
(E) Same situation as A. Despite the negative number, the x intercept is still positive.

sm176811 · Answer

Answer is B...

I found drawing the graph easier than solving it using y=mx+c!

shevy · Answer

Agree with B :wink:

Line L passes through point (1,4) and the product of its

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