Answer:

y=frac{-3}{4} x+36

Step-by-step explanation:

Since we are given that the railing will begin at a height of 36 inches and follow the slant of the stairs, which decreases 9 vertical inches for every 12 horizontal inches.

Thus the rate of change :  frac{-9}{12} =frac{-3}{4}

Rate of change represents the slope of line.

Since we are given that height, y, of the railing in inches according to the horizontal distance in inches, x, from the top of the stairs

And the initial height of the railing was 36 inches .

So,the function which would represent the situation can be shown using equation of line :

y = mx+c

So m=frac{-3}{4}

c = 36 inches

So, the function : y=frac{-3}{4} x+36

Hence The function which can represent the height, y, of the railing in inches according to the horizontal distance in inches, x, from the top of the stairs :

y=frac{-3}{4} x+36