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 = –x 36 y = –3x 36 y = x 36 y = 3x 36

Answer 1

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

Explanation:

Since we are given that the railing will begin at a height of 36 inches and follow the slant of the stairs, which decreases 9 vertical inches for every 12 horizontal inches.

Thus the rate of change :
`(-9)/(12) =(-3)/(4)`

Rate of change represents the slope of line.

Since we are given that height, y, of the railing in inches according to the horizontal distance in inches, x, from the top of the stairs

And the initial height of the railing was 36 inches .

So,the function which would represent the situation can be shown using equation of line :

y = mx+c

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

c = 36 inches

So, the function :
`y=(-3)/(4) x+36`

Hence The function which 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=(-3)/(4) x+36`

Answer 2

*Keyword:

Slope, proportion, relationship, decrease, line equation

The key to answering this question is to understand what means that the height of the railing decreases 9 vertical inches per 12 inches horizontal. This ratio represents the slope of the railing and therefore the slope of the line equation. We can write the relationship as follows:

`(y)/(x) = (-9)/(12)\\\\(y)/(x) = (-3)/(4)\\\\y = (-3)/( 4)x`

Then the slope
`m = -(3)/(4)`.

In general, the equation of a line is:

`y = mx + b`.

Where:

m = slope

b = cut point with the y axis

Then, we know that the initial height of the railing is 36 inches. This means that the greatest value that the variable y can take is 36. This value must occur when the value of x (the horizontal length) is minimum (equal to 0). Therefore 36 is the cutoff point with the y axis. b = 36

Finally, the equation sought is:

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

Answer

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