METEOROLOGY In stable air, as the altitude of a weather...

METEOROLOGY In stable air, as the altitude of a weather balloon increases, the temperature drops at a rate of about $5^{\circ} \mathrm{F}$ for each 1,000 -foot rise in altitude. (A) If the temperature at sea level is $70^{\circ} \mathrm{F}$, write a linear equation that expresses the temperature $T$ in terms of altitude $A$ (in thousands of feet above sea level). (B) What would the temperature be at an altitude of 10,000 feet? (C) What is the slope of the graph of the equation found in part A? What does the slope describe physically?

METEOROLOGY In stable air, as the altitude of a weather balloon increases, the temperature drops at a rate of about $5^{\circ} \mathrm{F}$ for each 1,000 -foot rise in altitude.
(A) If the temperature at sea level is $70^{\circ} \mathrm{F}$, write a linear equation that expresses the temperature $T$ in terms of altitude $A$ (in thousands of feet above sea level).
(B) What would the temperature be at an altitude of 10,000 feet?
(C) What is the slope of the graph of the equation found in part A? What does the slope describe physically?

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Key Concepts

Y-Intercept

The y-intercept is the value of the dependent variable when the independent variable is zero. It often represents the initial or starting condition in a modeled relationship, serving as a reference point to determine subsequent changes as the independent variable increases or decreases.

Slope and Rate of Change

The slope in a linear equation quantifies the rate of change between the two variables—it indicates how much the dependent variable changes for each unit change in the independent variable. In physical contexts, this concept is essential for understanding and quantifying consistent changes, such as a regular decrease or increase in a measured parameter.

Linear Equations

A linear equation represents a relationship between two variables with a constant rate of change and can be written in the form y = mx + b, where m is the slope and b is the y-intercept. This form is widely used in various fields to model situations where changes occur at a steady pace.

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