Question

writing an equation to represent a real - world problem
caitlin is designing a railing for a set of stairs. the railing will begin at a height of 36 inches and follow the slant of the stairs, which decreases 9 inches for every 12 horizontal inches.
which function can represent the height y, of the railing in inches according to the horizontal distance in inches, x, from the top of the stairs?
$y = -\frac{3}{4}x + 36$
$y = - 3x + 36$
$y=\frac{3}{4}x + 36$
$y = 3x + 36$

Explanation:

Step1: Identify initial height (y-intercept)

The starting height is 36 inches, so $b=36$ in $y=mx+b$.

Step2: Calculate slope (rate of change)

Height decreases 9 in per 12 horizontal in: $m=\frac{-9}{12}=-\frac{3}{4}$

Step3: Form linear equation

Substitute $m$ and $b$ into $y=mx+b$: $y=-\frac{3}{4}x+36$

Answer:

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