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?\n\\(\\frac{1}{3}\\) inch up per foot across\n\\(\\frac{1}{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?\n\\(\\frac{1}{3}\\) inch up per foot across\n\\(\\frac{1}{2}\\) inch up per foot across\n2 inches up per foot across\n3 inches up per foot across

Answer

Explanation:

Step1: Recall slope formula

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

Step2: Substitute values into formula

$m=\frac{18 - 12}{6 - 4}=\frac{6}{2}=3$.

Answer:

3 inches up per foot across