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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Quantity B is greater.

The longer the side opposite an angle, the larger the angle itself must be. Angle C open to the longest side, so is greater than angle A.

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.

No you are correct! We are not suppose to assume that diagram is to scale. However the basic shapes in the diagram are valid such as point B is above line AC (away from x axis).

You could argue that slope of line AB is greater because point B lies above line AC and thus a higher slope.

Not that in both the cases the lines AB and AC made acute angles with the x axis.
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Line is steeper means bigger slope so option A is correct as line AB is steeper
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For line AB, the y- intercept is higher than for line AC. Thus the slope for line AB is greater than slope for line AC.

Hence Qt A > Qt B

Both the lines have positive slopes [as they are going from left to right in up direction]
Slope of the line closer to y-axis has greater slope.

Hence A is correct
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