Coordinate Geometry DS – Slope of Lines

Is the slope ‘m’ of the line y = mx + c positive?
1. The x and y intercepts are both negative.
2. The line passes through the first quadrant.

Correct Answer : Choice A. Statement 1 alone is sufficient.

Explanatory Answer

Positive Sloping Lines : The x and y intercepts of the line are of opposite signs. If the x intercept is positive, the y intercept will be negative. Conversely if the y intercept is positive, the x intercept will be negative.

 Negative Sloping Lines : The x and y intercept will be of the same sign. If the x intercept is positive, the y intercept will also be positive. If the x intercept is negative, the y intercept will also be negative.

Statement 1 : x and y intercepts are both negative. The line has to be a negative sloping line. So, we can answer from statement 1 that the line is not positive sloping. 

Statement 1 is sufficient. Choice A or Choice D is the answer.

Statement 2: The line passes through the first quadrant. Knowing only one of the quadrants through which a line passes we will not be able to determine whether it is positive sloping. Statement 2 is not sufficient.

As statement 1 alone is sufficient, while statement 2 is not choice A is the correct answer.