Question

A ramp with a constant incline is made to connect a driveway to a front door. At a point 4 feet from the driveway, the height of the ramp is 12 inches. At a point 6 feet from the driveway, the height of the ramp is 18 inches. What is the rate of change of the ramp’s incline?

inch up per foot across
inch up per foot across
2 inches up per foot across
3 inches up per foot across

Answer 1

welcome to QC!!!

since we need to find the rate of change, we do this two ways.

the first way is to find the slope of the ramp.
we have TWO points given to us : (4,12) and (6,18)

now we do the slope formula:
\[\frac{ y2-y1 }{ x2-x1 }=\frac{ 18-12 }{ 6-4 }=\frac{ 6 }{ 2 }=3\]

our slope is 3 which means 3 inches per foot.


we could also find the unit rate.

since we have the point (4,12), meaning up 12 inches at 4 feet, we need to find how many inches up it is at ONE foot.

to do this we do:
\[\frac{ 12 }{ 4 }=\frac{ ? }{ 1 }\]

all that is left to do is divide.

what is 12/4?

Answer 2

\(\color{#0cbb34}{\text{Originally Posted by}}\) @mxddi3
welcome to QC!!!

since we need to find the rate of change, we do this two ways.

the first way is to find the slope of the ramp.
we have TWO points given to us : (4,12) and (6,18)

now we do the slope formula:
\[\frac{ y2-y1 }{ x2-x1 }=\frac{ 18-12 }{ 6-4 }=\frac{ 6 }{ 2 }=3\]

our slope is 3 which means 3 inches per foot.


we could also find the unit rate.

since we have the point (4,12), meaning up 12 inches at 4 feet, we need to find how many inches up it is at ONE foot.

to do this we do:
\[\frac{ 12 }{ 4 }=\frac{ ? }{ 1 }\]

all that is left to do is divide.

what is 12/4?
\(\color{#0cbb34}{\text{End of Quote}}\)
Dang u good at explainin stuff!

Answer 3

\(\color{#0cbb34}{\text{Originally Posted by}}\) @WendyMorales2007
\(\color{#0cbb34}{\text{Originally Posted by}}\) @mxddi3
welcome to QC!!!

since we need to find the rate of change, we do this two ways.

the first way is to find the slope of the ramp.
we have TWO points given to us : (4,12) and (6,18)

now we do the slope formula:
\[\frac{ y2-y1 }{ x2-x1 }=\frac{ 18-12 }{ 6-4 }=\frac{ 6 }{ 2 }=3\]

our slope is 3 which means 3 inches per foot.


we could also find the unit rate.

since we have the point (4,12), meaning up 12 inches at 4 feet, we need to find how many inches up it is at ONE foot.

to do this we do:
\[\frac{ 12 }{ 4 }=\frac{ ? }{ 1 }\]

all that is left to do is divide.

what is 12/4?
\(\color{#0cbb34}{\text{End of Quote}}\)
Dang u good at explainin stuff!
\(\color{#0cbb34}{\text{End of Quote}}\)
lol, thank you sm !