VERBAL1 wrote:
In the xy plane, if line k has a negative slope and passes through the point (s, -2), is the x-intercept of the line k positive?
1) s=0
2) The y-intercept of the line k is negative
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Line k passes through the point (s,-2) and has negative slope
Concept tested -> If slope is negative, then line makes >90 degree angle and less than 180 degree angle with respect to z-axis when measured in anti-clockwise direction.
Hence we know that line's angle against z-axis lies in the above mentioned range.
Now let's analyse each statement
Statement 1 -> It says s=0, thus we know that the coordinate point lies below origin and on y-axis, and to maintain the negative slope, line has to maintain an angle that is greater than 90° but less than 180°. Clearly X intercept will be negative in this case, thus statement 1 is sufficient.
We can drop option B and E now.
Let's analyse statement 2
Statement 2 tells us that y intercept is negative, we can visualize this as the case when line k passes the XY plane below origin
And the case becomes same as statement -> s=0 -> (0,-2) means negative y intercept -> X is negative
Hence statement 2 is also sufficient.
Thus, both statements are sufficient independently
Our answer is option D