There is some confusion in the phrase, "By tweaking the time sweep, the periodic saw-tooth voltage of the oscilloscope is replaced. . ."
I assume this means that, instead of using the time base saw tooth to drive the horizontal deflection, you use an external sinusoidal input signal to drive the horizontal deflection. If I am correct about this, then it is a very poorly worded question, and the result would be a diagonal line on the screen, since, at every moment, the vertical deflection would coincide with a proportional horizontal deflection. I think the external horizontal input deflects to the right, for a positive voltage, so the diagonal would by low on the left and high on the right.
If the horizontal amplifier was set to the same deflection sensitivity as the vertical input amplifier, the diagonal would have a slope of 45 degrees.