From the figure we can see that \(AB\) and \(AC\) have the same common point \(A\)

A nice point to compare the slope would be the x-axis.
At this point change is \(Y\) is same for both the line from point \(A\)
however, change in \(x\) for \(AB\) is smaller than \(AC\) therefore slope of qty A is greater than qty B
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This is my response to the question and may be incorrect. Feel free to rectify any mistakes

How did you define in the above diagram longer side. As per ETS we should not assume any angle or length unless specified.

In fact, to solve this question one must bear in mind that slope is read from left to right. The steeper it is the bigger its slope, because in the above diagram,
the slope AB is steeper than slope AC beacause when u read it from left to right AC is not steeper than AB and hence AB is bigger than AC.Hence option A is correct.

Please rectify if I am wrong.