Math Problem Statement

The graph models the linear relationship between the temperature of Earth’s atmosphere and the altitude above sea level.

What is the rate of change of the temperature with respect to altitude?

_____°C/km

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Solution

The rate of change of the temperature with respect to altitude is essentially the slope of the line on the graph. The slope can be found by identifying two points on the line and using the formula:

slope=change in temperaturechange in altitude=ΔTΔh\text{slope} = \frac{\text{change in temperature}}{\text{change in altitude}} = \frac{\Delta T}{\Delta h}

Where:

  • ΔT\Delta T is the change in temperature (in °C),
  • Δh\Delta h is the change in altitude (in kilometers).

Do you have the graph or two specific points from it so we can calculate the slope? Or can you describe the points where the line intersects the axes or any two points on the graph?

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Math Problem Analysis

Mathematical Concepts

Linear Relationships
Slope
Rate of Change

Formulas

slope = ΔT / Δh

Theorems

Slope formula for linear equations

Suitable Grade Level

Grades 8-10