Given:
The railing will begin at a height of 36 inches.
Height decreases 9 inches for every 12 horizontal inches.
To find:
The function for this situation.
Solution:
Let y be the height of the railing in inches according to the horizontal distance in inches, x, from the top of the stairs.
Initial height = 36
So, y-intercept is 36.
Height decreases 9 inches for every 12 horizontal inches. So,
![\text{Slope}=\dfrac{\text{Vertical change}}{\text{Horizontal change}}](https://tex.z-dn.net/?f=%5Ctext%7BSlope%7D%3D%5Cdfrac%7B%5Ctext%7BVertical%20change%7D%7D%7B%5Ctext%7BHorizontal%20change%7D%7D)
![m=\dfrac{-9}{12}](https://tex.z-dn.net/?f=m%3D%5Cdfrac%7B-9%7D%7B12%7D)
![m=-\dfrac{3}{4}](https://tex.z-dn.net/?f=m%3D-%5Cdfrac%7B3%7D%7B4%7D)
Slope intercept form of a line is
![y=mx+b](https://tex.z-dn.net/?f=y%3Dmx%2Bb)
Substitute
and b=36.
![y=-\dfrac{3}{4}x+36](https://tex.z-dn.net/?f=y%3D-%5Cdfrac%7B3%7D%7B4%7Dx%2B36)
The required function is
.
Therefore, the correct option is A.