Question

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.
A drawing of the side view of a set of 4 stairs. There are lines drawn to show a railing that is at the highest point of the stairs and labeled 36 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 = –StartFraction 3 Over 4 EndFractionx + 36
y = –3x + 36
y = StartFraction 3 Over 4 EndFractionx + 36
y = 3x + 36

Answer 1

Answer:

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

Step-by-step explanation:

Givens

• The railing will begin at 36 inches height.
• The slant decreases 9 inches for every 12 horizontal inches.

According to the problem, the slant is

$m=-\frac{9}{12}=-\frac{3}{4}$

The initial condition of the function is 36, which is a constant. Also, the slant is negative, because the problem states that "decreases".

If we see the problem form the perspective of a linear function, the constant ratio of change would be the slant.

Therefore, the linear function that models this problem is

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

So, the answer is the first choice.

Answer 2

Answer:

first option

Step-by-step explanation: