\(3\) inches up per foot across

UpStudy Free Solution:

To determine the rate of change of the ramp's incline, we need to calculate the slope of the ramp. The slope is given by the change in height (rise) divided by the change in horizontal distance (run).

Given data:

- At 4 feet from the driveway, the height is 12 inches.

- At 6 feet from the driveway, the height is 18 inches.

Let's calculate the rise and run:

1. Calculate the rise:

\(\text { Rise} = \text { Height at 6 feet} - \text { Height at 4 feet} = 18 \text { inches} - 12 \text { inches} = 6 \text { inches} \)

2. Calculate the run:

\(\text { Run} = 6 \text { feet} - 4 \text { feet} = 2 \text { feet} \)

3. Calculate the slope (rate of change):

\(\text { Slope} = \frac { \text { Rise} } { \text { Run} } = \frac { 6 \text { inches} } { 2 \text { feet} } = 3 \text { inches per foot} \)

Key Concepts:

1. Slope (Rate of Change): The slope of a line (or ramp) represents the rate of change of the vertical distance (rise) compared to the horizontal distance (run). It is calculated using the formula:

\(\text { Slope} = \frac { \text { Rise} } { \text { Run} } \)

2. Units: Ensure the units are consistent when calculating slope. Convert measurements if necessary to avoid errors.

The ability to find the slope is something that has actual world usefulness for determining the steepness or incline of ramps and like that. For a more personalized experience and much more elaborated, step-by-step help in geometry and algebra problems, make sure you have UpStudy Math Solver. From carefully detailed descriptions to solution-specific direction, UpStudy makes sure that you understand anything and everything. Discover all the ways UpStudy can assist you in learning now!