157. If line L passes through point (m, n) and
(– m, – n), where m and n are not 0, which of the following must be true?
I. The slope of L is positive
II. The slope of L is negative
III. L exactly passes through 2 quadrants
(A) I only
(B) II only
(C) III only
(D) I and II only
(E) II and III only
Equation of the line with slope m passing through point \((x_1,y_1)\) \(&\) \((x_2,y_2)\)
We have the line that is passing through \((m,n)\) \(&\) \((-m,-n)\)
Equation of the line will be:
Thus we know that this line passes through the origin as the y-intercept is 0. This makes III true.
If we put, n=1 and m=1
\(y=x\); this line has a positive slope. We can count II out.
Put n=-1 and m=1
\(y=-x\); this line has negative slope. We can count I out.
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