a ramp with a constant incline is made to connect a driveway to a front door. at a point 4 feet from the…

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 ramps incline?\n1/3 inch up per foot across\n1/2 inch up per foot across\n2 inches up per foot across\n3 inches up per foot across

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 ramps incline?\n1/3 inch up per foot across\n1/2 inch up per foot across\n2 inches up per foot across\n3 inches up per foot across

Answer

Explanation:

Step1: Identify two - point data

We have two points: (4 feet, 12 inches) and (6 feet, 18 inches).

Step2: Use the slope formula

The slope formula for rate of change is $m=\frac{y_2 - y_1}{x_2 - x_1}$, where $(x_1,y_1)$ and $(x_2,y_2)$ are two points. Here, $x$ is the horizontal distance from the driveway (in feet) and $y$ is the height of the ramp (in inches). So $x_1 = 4$, $y_1=12$, $x_2 = 6$, $y_2 = 18$. Then $m=\frac{18 - 12}{6 - 4}$.

Step3: Calculate the slope

$\frac{18 - 12}{6 - 4}=\frac{6}{2}=3$ inches per foot.

Answer:

3 inches up per foot across