Two lines, k and m, intersect in the coordinate plane at point (a,b).

Here's the explanation for option B

We are told that both Lines m and k have positive slopes. Any line with a positive slope will slope upwards i.e. will be tilted from left to right. See the figure attached.
We are also told (in the given question) that the x-intercept of k and y-intercept of m are both positive. So, there's only one i.e. unique way to draw these two lines. They are drawn as shown in the attached figure.

Hence, it is quite clear from the diagramming that the point of intersection of these two lines (m and k) considering that they have different slopes, lies in the Third Quadrant, as shown in the figure.

Hence, as 'a' and 'b' both are negative, the product 'ab' is positive. Hence this Statement is sufficient to answer the question alone.
Hope you've already figured out that Statement 1 is also sufficient by itself to answer the question.

Hence the final answer is Option D.

Hope this helps.

Cheers!