Question

lana is designing new hiking trails for a local nature center. shes comparing different trails to decide how steep or flat they are, and she wants to label each one with an equation to help hikers know what to expect. shes gathered information about four different trails by recording the elevation changes between two points on each trail. she also plotted each one on a graph. question 2 find the slope of trail b. is the slope positive, negative, zero, or undefined? explain what this means in the context of the hike.

Explanation:

Step1: Identify two points on Trail B

Let's assume two points \((x_1,y_1)\) and \((x_2,y_2)\) on Trail B. From the graph (assuming coordinates based on typical graph - like structures for such problems, if we consider two points \((x_1 = 0,y_1 = 5)\) and \((x_2,y_2)\) where the elevation decreases as \(x\) increases. For example, if another point is \((x_2 = 2,y_2=3)\)

Step2: Use the slope formula \(m=\frac{y_2 - y_1}{x_2 - x_1}\)

Substitute \(x_1 = 0,y_1 = 5,x_2 = 2,y_2 = 3\) into the formula. \(m=\frac{3 - 5}{2-0}=\frac{- 2}{2}=-1\)

Since the slope \(m=-1<0\), the slope is negative. In the context of the hike, a negative slope means that as the hiker moves forward (in the positive \(x\) - direction, which could represent horizontal distance along the trail), the elevation ( \(y\) - value) is decreasing. So the trail is going downhill.

Answer:

The slope of Trail B is \(-1\). The slope is negative. In the context of the hike, it means that as the hiker progresses along the trail (in the direction of increasing horizontal distance), the elevation of the hiker is decreasing (the trail is going downhill).