In the xy-plane, if line k has negative slope, is the y-intercept of line k positive?
(1) The x-intercept of line k is less than the y-intercept of line k.
(2) The slope of line k is less than -2.
OA C
Source: Veritas Prep
In the xy-plane, if line k has negative slope, is the
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Say the equation of the line is y = mx + c, where m is the slope and c is the y-intercept of the lineBTGmoderatorDC wrote:In the xy-plane, if line k has negative slope, is the y-intercept of line k positive?
(1) The x-intercept of line k is less than the y-intercept of line k.
(2) The slope of line k is less than -2.
OA C
Source: Veritas Prep
Since it is given that line k has a negative slope, we have m < 0
Thus, we can write the equation as y =-|m|x + c
We have to determine whether c < 0.
Let's take each statement one by one.
(1) The x-intercept of line k is less than the y-intercept of line k.
Rewriting the equation y =-|m|x + c as y - c = -|m|x
=> [-1/|m|]*y + c/|m| = x
Thus, we have x-intercept of the line k = c/|m|
From the given information, we have c/|m| < c. This information is insufficient since c may or may not be positive. Insufficient.
(2) The slope of line k is less than -2.
=> -|m| < -2 => |m| > 2. Insufficient to determine wether c < 0.
(1) and (2) together
From (1), we have c/|m| < c and from (2), we have |m| > 2. Let's assume that y-intercept c is positive. Thus, we have
If c is positive, from the given inequality c/|m| < c, we cancel c; thus, we have 1/|m| < 1, which is possible since |m| > 2.
The y-intercept c cannot be negative. let's see how.
If c is negative, from the given inequality c/|m| < c, we have [-c/|m|] < -c. We can cancel c; thus, we have -1/|m| < -1, which is NOT possible since |m| > 2.
Thus, c > 0. Sufficient.
The correct answer: C
Hope this helps!
-Jay
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