Question

writing an equation to represent
a railing for a set of stairs. the railing
of a height of 36 inches and follows the slant of
which decreases 9 inches for every 12
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{1}{4}x + 36 \\)
\\( y = -3x + 36 \\)
\\( y = \frac{1}{4}x + 36 \\)
\\( y = 3x + 36 \\)

Explanation:

Step1: Identify slope (rate of change)

The height decreases 9 inches for 12 horizontal inches, so slope $m = \frac{-9}{12} = -\frac{3}{4}$.

Step2: Identify y-intercept

At $x=0$ (top of stairs), height $y=36$, so y-intercept $b=36$.

Step3: Write linear function

Use slope-intercept form $y=mx+b$.
$y = -\frac{3}{4}x + 36$

Answer:

$y = -\frac{3}{4}x + 36$ (the first option)