Question

what is the slope of the line and what does it mean in this situation?
the slope is -500. this means that the bird descends 500 m each minute.
the slope is -350. this means that the bird descends 350 m each minute.
the slope is 350. this means that the bird ascends 350 m each minute.
the slope is 500. this means that the bird ascends 500 m each minute.

Explanation:

Step1: Recall the slope formula

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$.

Step2: Identify two points

We can use the points $(2,5000)$ and $(5,3500)$. Here, $x_1 = 2,y_1=5000,x_2 = 5,y_2 = 3500$.

Step3: Calculate the slope

Substitute into the formula: $m=\frac{3500 - 5000}{5 - 2}=\frac{-1500}{3}=-500$.

Step4: Interpret the slope

Since the slope is negative, it represents a descent. The magnitude $500$ means the bird descends $500$ meters per minute.

Answer:

A. The slope is $-500$. This means that the bird descends $500$ m each minute.