Question

zane is a dangerous fellow who likes to go rock climbing in active volcanoes. one time, when he was 20 meters below the edge of a volcano, he heard some rumbling, so he decided to climb up out of there as quickly as he could. he managed to climb up 4 meters each second and get out of the volcano safely. graph the relationship between zanes elevation relative to the edge of the volcano (in meters) and time (in seconds). elevation (meters) 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 time (seconds) -2 -6 -8 -10 -12 -14 -16 -18 -20

Explanation:

Step1: Define Variables and Equation

Let \( t \) be time in seconds and \( y \) be elevation (meters, negative below edge). Initial elevation: \( y(0) = -20 \). Rate: \( 4 \, \text{m/s} \) up, so \( y = -20 + 4t \).

Step2: Find Key Points

• At \( t = 0 \): \( y = -20 \) (point: \( (0, -20) \)).
• At \( t = 5 \): \( y = -20 + 4(5) = 0 \) (point: \( (5, 0) \)).

Step3: Graph the Line

Plot \( (0, -20) \) and \( (5, 0) \), then draw a straight line through them. The line has slope \( 4 \), starting at \( (0, -20) \) and rising to \( (5, 0) \).

Answer:

The graph is a straight line connecting \((0, -20)\) and \((5, 0)\) with a slope of \(4\), representing \(y = -20 + 4t\) (elevation vs. time).