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. 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

A

Explanation:

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 2

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}=\frac{\text{Vertical change}}{\text{Horizontal change}}`

`m=(-9)/(12)`

`m=-(3)/(4)`

Slope intercept form of a line is

`y=mx+b`

Substitute
`m=-(3)/(4)` and b=36.

`y=-(3)/(4)x+36`

The required function is
`y=-(3)/(4)x+36`.

Therefore, the correct option is A.