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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.
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.