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...Fractions are completely normal. In fact, I don't see how you can have a slope that isn't one. Your slope is basically your rise/run. Suppose your slope was 2/3. 2 would be your rise(how much you go up on the y-axis), and 3 would be your run(how much you go across on your x-axis). Even if you got something like 5, that is still the same as 5/1.

...So, yes. A slope can be a fraction. I think your teacher meant you shouldn't get something like 2.4/5. I hope that helped

A slope can most definitely be a fraction.

Here's an example:

y = -5/3x - 2/3

yes it can because it is rise over run