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Slope, m, is equal to the ratio between the change in y and the change in x

m =  \frac{\Delta y}{\Delta x}

m ≤ 3/4      (green line in the attached illustration)
Δx = 0.83 ft
Δy represents the height of each step (red lines in the attached illustration)

\frac{3}{4} = \frac{\Delta y}{0.83}

\Delta y =  \frac{3}{4}(0.83)

\Delta y = 0.6225

The height of each step should be 0.6225 ft.

Since the whole staircase measures 9 ft high, 
9 ÷ 0.6225 = 14.45
There should be 14.45* steps in the staircase.

*This seems illogical because how can you have a 0.45 step, right?
Since the problems says that the slope CANNOT exceed 3/4 (it did not say that the slope is EQUAL to 3/4), we may change the slope of the line such that we will get an integer for the number of steps.
I worked backwards and found out that using m=60/83 (which is less than 3/4, and thus satisfies the given condition) will give a better result:

m = \frac{\Delta y}{\Delta x}

\frac{60}{83} = \frac{\Delta y}{0.83}

\Delta y = \frac{60}{83}(0.83)

\Delta y = 0.6

The height of each step will be 0.6 ft.

9 ÷0.6 = 15

So, there will be a total of 15 steps in the staircase.
2 5 2
Btw, Δy and Δx (Δ read as delta) means the same as y1-y2 and x1-x2
Thank you so much!!!!!
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