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. Write a linear equation that represents the situation.

A) y = 2x
B) y = 3x
C) y = 6x
D) y = 4x

Answer 1

The correct linear equation that represents the ramp's situation is B) y = 3x, determined by finding the slope between two given points on the ramp.

Step-by-step explanation:

To write a linear equation that represents the situation of a ramp connecting a driveway to a front door with the given heights at different points, we need to find the slope and the y-intercept of the equation. We are given two points: (4, 12) and (6, 18). The slope ("m") is calculated by the rise over the run, which in this case is "(change in height) / (change in distance)" between the two points. The slope will be:

"m = (18 - 12) / (6 - 4) = 6 / 2 = 3

Therefore, the slope of the ramp is 3. A linear equation with this slope and no y-intercept provided would be "y = 3x", assuming that the ramp starts from the ground level at the driveway. The correct linear equation representation from the given options is B) y = 3x.