Question

balloons
400
300
200
100
0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
minutes since noon
what does the slope of the line tell you about the situation?
the balloons altitude increases 150 feet every minute.
the balloons altitude increases 100 feet every minute.
the balloons altitude is 400 feet after 2 minutes.
the balloons altitude is 700 feet after 4 minutes.

Explanation:

Step1: Recall slope formula

The slope \( m \) of a line is calculated as \( m=\frac{y_2 - y_1}{x_2 - x_1} \), where \( (x_1,y_1) \) and \( (x_2,y_2) \) are two points on the line.
From the graph, we can take two points: when \( x_1 = 0 \) (noon, 0 minutes), \( y_1=100 \) (altitude 100 feet); when \( x_2 = 2 \), \( y_2 = 400 \).

Step2: Calculate the slope

Substitute into the slope formula: \( m=\frac{400 - 100}{2 - 0}=\frac{300}{2}=150 \).
This means the balloon's altitude increases by 150 feet for each minute (since slope represents the rate of change of \( y \) with respect to \( x \), here \( y \) is altitude and \( x \) is time in minutes).
Now check the options:

• "The balloon's altitude increases 150 feet every minute." matches the slope calculation.
• "The balloon's altitude increases 100 feet every minute." has a wrong rate.
• "The balloon's altitude is 400 feet after 2 minutes." is a fact from the graph but not about the slope (slope is about rate, not a specific point's value).
• "The balloon's altitude is 700 feet after 4 minutes." Let's verify: using the slope \( 150 \), starting from 100, after 4 minutes: \( 100+150\times4 = 100 + 600=700 \). But this is also a specific point, not about the slope (rate of change). The question asks what the slope tells about the situation (rate of change), so the first option is correct.

Answer:

The balloon's altitude increases 150 feet every minute.