Question

the elevation e (in feet) of a hot air balloon and its time t (in minutes) are related by a linear equation. consider the graph of this equation, with time represented on the horizontal axis and elevation on the vertical axis. finally, think about this scenario. is the slope positive, zero, or negative? the hot air balloon is at an elevation of 300 feet and is ascending at a constant rate of 900 feet per minute. the slope is dropdown .

Explanation:

Step1: Recall Slope Definition

Slope is $\frac{\text{change in } y}{\text{change in } x}$. Here, $y$ (elevation $e$) and $x$ (time $t$).

Step2: Analyze Rate of Change

The balloon ascends (elevation increases) at 900 ft/min. So as $t$ (time) increases, $e$ (elevation) increases.

Step3: Determine Slope Sign

Since $\text{change in } e$ (vertical) and $\text{change in } t$ (horizontal) are both positive, slope $=\frac{\text{positive}}{\text{positive}}=$ positive.

Answer:

positive